{"id":4149,"date":"2022-09-23T18:51:57","date_gmt":"2022-09-23T18:51:57","guid":{"rendered":"https:\/\/www.studyzonebd.com\/math\/?p=4149"},"modified":"2022-09-23T19:30:55","modified_gmt":"2022-09-23T19:30:55","slug":"class-six-chapter-04-lesson-4-3","status":"publish","type":"post","link":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/","title":{"rendered":"\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983\u00a0\u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 | \u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf"},"content":{"rendered":"\n

\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u09ec\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Six (06) Math <\/a>Book Solution | Chapter <\/a>04 : Algebraic Expressions | Online Solution<\/p>\n\n\n\n

\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 : \u09b8\u09a6\u09c3\u09b6 \u0993 \u09ac\u09bf\u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6 \u0993 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u09b0\u09af\u09cb\u0997 \u09ac\u09bf\u09af\u09bc\u09cb\u0997<\/h4>\n\n\n\n

\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 \u098f\u09b0 \u09b8\u0995\u09b2 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u0989\u09a4\u09cd\u09a4\u09b0 \u098f\u0996\u09be\u09a8\u09c7 \u09b0\u09df\u09c7\u099b\u09c7\u0964 \u09ec\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/p>\n\n\n\n

\u09ec\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf\u09b0 \u0997\u09a3\u09bf\u09a4 \u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/span><\/h4>\n\n\n\n

\u09af\u09cb\u0997 \u0995\u09b0\u0983<\/a><\/p>\n\n\n\n

\u09e7. 5x+3y \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09a4\u09c7 x \u098f\u09b0 \u09b8\u09b9\u0997 \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf?<\/strong><\/p>\n\n\n\n

(\u0995) 8    (\u0996) 5x<\/p>\n\n\n\n

(\u0997) 3y   (\u0998) 5
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0998<\/p>\n\n\n\n

\u09e8. x \u098f\u09b0 \u09a4\u09bf\u09a8\u0997\u09c1\u09a3 \u098f\u09ac\u0982 y \u098f\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf?<\/strong><\/p>\n\n\n\n

(\u0995) y+3x  (\u0996) 3x+2y<\/p>\n\n\n\n

(\u0997) x+2y  (\u0998) 2x+3y
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09e9. 7x3<\/sup><\/strong>\u2715<\/strong>x2<\/sup> \u098f \u098f\u09b0 \u09b8\u09c2\u099a\u0995 \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf?<\/strong><\/p>\n\n\n\n

(\u0995) 7     (\u0996) 5
(\u0997)  x5<\/sup>   (\u0998) x6
<\/sup>\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09ea. \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8 \u099c\u09cb\u09a1\u09bc\u09be \u09b8\u09a6\u09c3\u09b7 \u09aa\u09cd\u09aa\u09a6 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7?<\/strong><\/p>\n\n\n\n

(\u0995) 2x, -7xy     (\u0996) -3xy, 7x2<\/sup>y
(\u0997) 3x2<\/sup>, -7x2<\/sup>    (\u0998) -7x2<\/sup>y, 8xy2
<\/sup>\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0997<\/p>\n\n\n\n

\u09eb. M2-7 \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09a4\u09c7 m=-6 \u09b9\u09b2\u09c7, \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 36   (\u0996) 13
(\u0997) -29  (\u0998) 29
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0998<\/a><\/p>\n\n\n\n

\u09ec. a-b \u09a5\u09c7\u0995\u09c7 b-a \u09ac\u09bf\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09b2\u09c7, \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 \u0995\u09a4 \u09b9\u09ac\u09c7?<\/strong><\/p>\n\n\n\n

(\u0995) a+b    (\u0996) 0
(\u0997) 2a-2b  (\u0998) a
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0997<\/p>\n\n\n\n

\u09ed. x2<\/sup>+3, x2<\/sup>-2, -2x2<\/sup>+1 \u09b0\u09be\u09b6\u09bf \u09a4\u09bf\u09a8\u099f\u09bf\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 1        (\u0996) 2
(\u0997)  x2<\/sup>-1   (\u0998) 1-x2
<\/sup>\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09ee. 5x4<\/sup> \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09a4\u09c7\u2014<\/strong><\/p>\n\n\n\n

i.  x \u098f\u09b0 \u0998\u09be\u09a4 4
ii.  \u09a6\u09c1\u0987\u099f\u09bf \u09aa\u09a6 \u0986\u099b\u09c7
iii.  x4<\/sup> \u098f\u09b0 \u09b8\u09b9\u0997 5<\/p>\n\n\n\n

\u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf \u09b8\u09a0\u09bf\u0995?<\/p>\n\n\n\n

(\u0995) i \u0993 ii     (\u0996) i \u0993 iii
(\u0997) ii \u0993 iii    (\u0998) i, ii \u0993 iii
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09ef. x \u0993 y \u099a\u09b2\u0995\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0\u2014<\/strong><\/p>\n\n\n\n

i.  \u09af\u09cb\u0997\u09ab\u09b2 x+y
ii.  \u0997\u09c1\u09a3\u09ab\u09b2 xy
iii.  \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf x2<\/sup>-y2<\/sup><\/p>\n\n\n\n

\u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf \u09b8\u09a0\u09bf\u0995?<\/p>\n\n\n\n

(\u0995) i \u0993 ii       (\u0996) i \u0993 iii
(\u0997) ii \u0993 iii      (\u0998) i, ii \u0993 iii
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0995<\/p>\n\n\n\n

x2<\/sup>-y2<\/sup>, y2<\/sup>-z2<\/sup> \u098f\u09ac\u0982 z2<\/sup>-x2<\/sup>  \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u09b0 \u0986\u09b2\u09cb\u0995\u09c7 (\u09e7\u09e6-\u09e7\u09e7) \u09a8\u0982 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u09c7\u09b0 \u0989\u09a4\u09cd\u09a4\u09b0 \u09a6\u09be\u0993\u0983<\/strong><\/p>\n\n\n\n

\u09e7\u09e6. x=2 \u098f\u09ac\u0982 y=-3 \u09b9\u09b2\u09c7 \u09e7\u09ae \u09b0\u09be\u09b6\u09bf\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) -13     (\u0996) -5
(\u0997) 5         (\u0998) 13
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09e7\u09e7. \u09b0\u09be\u09b6\u09bf \u09a4\u09bf\u09a8\u099f\u09bf\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 0                     (\u0996) 2x2
<\/sup>(\u0997) 2x2<\/sup>+2y2<\/sup>+2z2<\/sup>  (\u0998) -2x2<\/sup>-2y2<\/sup>-2z2
<\/sup>\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0995<\/p>\n\n\n\n

\u09e7\u09e8. <\/strong><\/p>\n\n\n\n

(i) 12x \u09b9\u09b2\u09cb x \u098f\u09ac\u0982 12 \u098f\u09b0 \u0998\u09be\u09a4\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf
(ii) 4a3<\/sup> \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09a4\u09c7 a \u098f\u09b0 \u09b8\u09c2\u099a\u0995 3
(iii) 3x+4 \u09b0\u09be\u09b6\u09bf\u09a4\u09c7 x \u098f\u09b0 \u09b8\u09b9\u0997 3<\/p>\n\n\n\n

\u0989\u09aa\u09b0\u09c7\u09b0 \u09a4\u09a5\u09cd\u09af\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09a4\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf \u09b8\u09a0\u09bf\u0995?<\/p>\n\n\n\n

(\u0995) i \u0993 ii        (\u0996) i \u0993 iii
(\u0997) ii \u0993 iii       (\u0998) i, ii \u0993 iii
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0997<\/p>\n\n\n\n

\u09e7\u09e9. <\/strong><\/p>\n\n\n\n

(i) 5ax2<\/sup> \u098f\u09ac\u0982 -7x2<\/sup>a\u098f \u09aa\u09a6 \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09a6\u09c3\u09b6\u0964
(ii) 3x2<\/sup>+2x+y-5x \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09a4\u09c7 \u09ea\u099f\u09bf \u09aa\u09a6 \u0986\u099b\u09c7\u0964
(iii) a=2 \u098f\u09ac\u0982 b=3 \u09b9\u09b2\u09c7, 4a-b \u098f\u09b0 \u09ae\u09be\u09a8 \u09b9\u09ac\u09c7 5.<\/p>\n\n\n\n

\u0989\u09aa\u09b0\u09c7\u09b0 \u09a4\u09a5\u09cd\u09af\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09a4\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf \u09b8\u09a0\u09bf\u0995?<\/p>\n\n\n\n

(\u0995) i \u0993 ii        (\u0996) i \u0993 iii
(\u0997) ii \u0993 iii       (\u0998) i, ii \u0993 iii
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09e7\u09ea. 9x2<\/sup>, 8x2<\/sup>, 5y2<\/sup> \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7\u2014<\/strong><\/p>\n\n\n\n

(\u09e7) \u09b0\u09be\u09b6\u09bf \u09a4\u09bf\u09a8\u099f\u09bf\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 13     (\u0996) 14
(\u0997)  17     (\u0998) 22
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0998<\/p>\n\n\n\n

(\u09e8) \u09aa\u09cd\u09b0\u09a5\u09ae \u09a6\u09c1\u0987\u099f\u09bf \u09b0\u09be\u09b6\u09bf\u09b0 \u0997\u09c2\u09a8\u09ab\u09b2\u09c7\u09b0 \u0998\u09be\u09a4\u09c7\u09b0 \u09b8\u09c2\u099a\u0995 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 72      (\u0996) 17
(\u0997) 4         (\u0998) 0
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0997<\/p>\n\n\n\n

\u09e7\u09eb. x2<\/sup>+y2<\/sup>+z2<\/sup>, x2<\/sup>-y2<\/sup>+z2<\/sup>, -x2<\/sup>+y2<\/sup>-z2<\/sup> \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u0964 \u098f\u0987 \u09a4\u09a5\u09cd\u09af\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09a4\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 (\u09e7) \u09a5\u09c7\u0995\u09c7 (\u09ea) \u09a8\u09ae\u09cd\u09ac\u09b0 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u09c7\u09b0 \u0989\u09a4\u09cd\u09a4\u09b0 \u09a6\u09be\u0993\u0983<\/strong><\/p>\n\n\n\n

(\u09e7) \u09aa\u09cd\u09b0\u09a5\u09ae \u09a6\u09c1\u0987\u099f\u09bf \u09b0\u09be\u09b6\u09bf\u09b0 \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf \u09af\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf \u09b9\u09ac\u09c7?<\/strong><\/p>\n\n\n\n

(\u0995) \u2013x2<\/sup>+3y2<\/sup>-z2<\/sup>    (\u0996) 3x2<\/sup>-y2<\/sup>+3z2<\/sup>   
(\u0997) x2<\/sup>-3y2<\/sup>+z2<\/sup>      (\u0998) x2<\/sup>+y2<\/sup>+z2<\/sup>   
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0995<\/p>\n\n\n\n

(\u09e8) \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u09b0 y2<\/sup> \u098f\u09b0 \u09b8\u09b9\u0997 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 0      (\u0996) -1
(\u0997) 1       (\u0998) 2
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

(\u09e9) \u09b0\u09be\u09b6\u09bf \u09a4\u09bf\u09a8\u099f\u09bf\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

(\u0995) 3x2<\/sup>+y2<\/sup>+z2<\/sup>        (\u0996) 2x2<\/sup>+y2<\/sup>+z2<\/sup>     
(\u0997) x2<\/sup>+y2<\/sup>+z2<\/sup>         (\u0998) x2<\/sup>-y2<\/sup>+z2<\/sup>     
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0997<\/p>\n\n\n\n

(\u09ea) \u09aa\u09cd\u09b0\u09a5\u09ae \u09a6\u09c1\u0987\u099f\u09bf \u09b0\u09be\u09b6\u09bf\u09b0 \u09af\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u09a5\u09c7\u0995\u09c7 \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf \u09ac\u09bf\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 \u09a8\u09bf\u099a\u09c7\u09b0 \u0995\u09cb\u09a8\u099f\u09bf \u09b9\u09ac\u09c7?<\/strong><\/p>\n\n\n\n

(\u0995) 3x2<\/sup>+2y2<\/sup>-z2<\/sup>      (\u0996) 3x2<\/sup>-y2<\/sup>+3z2<\/sup>     
(\u0997) x2<\/sup>+2y2<\/sup>-2z2<\/sup>       (\u0998 )3x2<\/sup>+3y2<\/sup>+3z2<\/sup>     
\u0989\u09a4\u09cd\u09a4\u09b0\u0983 \u0996<\/p>\n\n\n\n

\u09af\u09cb\u0997 \u0995\u09b0 (\u09e7\u09ec-\u09e8\u09eb)<\/span><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8: \u09e7\u09ec. 3a + 4b, a + 3b
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,
3a + 4b
a + 3b<\/span>
4a + 7b [\u09af\u09cb\u0997 \u0995\u09b0\u09c7]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09af\u09cb\u0997\u09ab\u09b2 4a + 7b<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8: \u09e7\u09ed. 2a + 3b, 3a + 5b, 5a + 6b
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,
2a + 3b
3a + 5b
5a + 6b<\/span>
10a + 14b [\u09af\u09cb\u0997 \u0995\u09b0\u09c7]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09af\u09cb\u0997\u09ab\u09b2 10a + 14b<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8: \u09e7\u09ee. 4a \u2013 3b, \u2013 3a + b, 2a + 3b
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

4a \u2013 3b
\u2013 3a + b
2a + 3b<\/span>
3a + b [\u09af\u09cb\u0997 \u0995\u09b0\u09c7]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09af\u09cb\u0997\u09ab\u09b2 3a + b<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8: \u09e7\u09ef. 7x + 5y + 2z, 3x \u2013 6y + 7z, \u2013 9x + 4y + z
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983 <\/p>\n\n\n\n

7z+5y+2z
3x-6y+7z
-9x+4y+z
<\/span>x+3y+10z
\u2234\u09af\u09cb\u0997\u09ab\u09b2=x+3y+10z<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e8\u09e6.x2<\/sup> + xy + z, 3x2<\/sup> \u2013 2xy + 3z, 2x2<\/sup> + 7xy \u2013 2z<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,
  x2<\/sup> +   xy +  z
3x2<\/sup> \u2013 2xy + 3z
2x2<\/sup> + 7xy \u2013 2z<\/span>
6x2<\/sup> + 6xy + 2z     [\u09af\u09cb\u0997 \u0995\u09b0\u09c7]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 6x2<\/sup> + 6xy + 2z<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e8\u09e7. 4p2<\/sup> + 7q2<\/sup> + 4r2<\/sup>, p2<\/sup> + 3r2<\/sup>, 8q2<\/sup> \u20137p2 <\/sup>\u2013 r2<\/sup><\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,
4p2<\/sup> + 7q2<\/sup> + 4r2<\/sup>
p2<\/sup>            + 3r2<\/sup>
\u20137p2<\/sup> + 8q2 <\/sup> \u2013   r2<\/sup>
<\/span>\u20132p2<\/sup> + 15q2<\/sup> + 6r2  <\/sup> [\u09af\u09cb\u0997 \u0995\u09b0\u09c7]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 \u20132p2<\/sup> + 15q2<\/sup> + 6r2<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8: \u09e8\u09e8. 3a + 2b \u2013 6c, \u2013 5b + 4a + 3c, 8b \u2013 6a + 4c
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

3a + 2b \u2013 6c
4a \u2013 5b + 3c
\u2013 6a + 8b + 4c<\/span>
\u200da + 5b + c [\u09af\u09cb\u0997 \u0995\u09b0\u09c7 ]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09af\u09cb\u0997\u09ab\u09b2 a + 5b + c<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e8\u09e9. 2x3<\/sup> \u2013 9x2<\/sup> + 11x + 5, \u2013 x3<\/sup> + 7x2<\/sup> \u2013 8x \u2013 3, \u2013 x3<\/sup> + 2x2<\/sup> \u2013 4x + 1<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

2x3<\/sup> \u2013 9x2<\/sup> + 11x + 5
\u2013 x3<\/sup> + 7x2<\/sup> \u2013   8x \u2013 3
\u2013 x3<\/sup> + 2x2<\/sup> \u2013   4x + 1
<\/span>0  +   0  \u2013    x + 3     [\u09af\u09cb\u0997 \u0995\u09b0\u09c7 ]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 (\u2013 x + 3)<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8: \u09e8\u09ea. 5ax + 3by \u2013 14cz, \u2013 11by \u2013 7ax \u2013 9cz, 3ax + 6by \u2013 8cz
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

5ax + 3by \u2013 14cz
\u2013 7ax \u2013 11by \u2013 9cz
3ax + 6by \u2013 8cz
<\/span> ax \u2013 2by \u2013 31cz [\u09af\u09cb\u0997 \u0995\u09b0\u09c7 ]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09af\u09cb\u0997\u09ab\u09b2 ax \u2013 2by \u2013 31cz<\/p>\n\n\n\n

 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 : \u09e8\u09eb. <\/strong>x2<\/sup> \u2013 5x + 6, x2<\/sup> + 3x \u2013 2, \u2013 x2<\/sup> + x + 1, \u2013x2<\/sup> + 6x \u2013 5<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987,<\/p>\n\n\n\n

    x2<\/sup> \u2013 5x + 6
    x2<\/sup> + 3x \u2013 2
\u2013 x2<\/sup> +   x + 1
\u2013x2<\/sup> + 6x \u2013 5
<\/span>   0 + 5x + 0      [\u09af\u09cb\u0997 \u0995\u09b0\u09c7]
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 5x<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e8\u09ec. \u09af\u09a6\u09bf a2<\/sup> = x2<\/sup> + y2<\/sup> \u2013 z2<\/sup>, b2<\/sup> = y2<\/sup> + z2<\/sup> \u2013 x2<\/sup>, c2<\/sup> = x2<\/sup> + z2<\/sup> \u2013 y2<\/sup> \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, a2<\/sup> + b2<\/sup> + c2<\/sup> = x2<\/sup> + y2<\/sup> + z2<\/sup>.<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a2<\/sup> =  x2<\/sup> + y2<\/sup> \u2013 z2<\/sup>
b2<\/sup> =    x2 <\/sup>+ y2<\/sup> + z2<\/sup>
c2<\/sup> =    x2<\/sup> \u2013 y2<\/sup> + z2<\/sup><\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7 = a2<\/sup> + b2<\/sup> + c2<\/sup>
= (x2<\/sup> + y2<\/sup> \u2013 z2<\/sup>) + (-x2<\/sup> + y2<\/sup> + z2<\/sup>) + (x2<\/sup> \u2013 y2<\/sup> + z2<\/sup>)   [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
= x2<\/sup> + y2<\/sup> \u2013 z2<\/sup> \u2013 x2  <\/sup>+ y2<\/sup> + z2<\/sup> + x2 <\/sup>\u2013 y2 <\/sup>+ z2<\/sup>
= x2<\/sup> + y2<\/sup> + z2<\/sup>
= \u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7
\u2234 a2<\/sup> + b2<\/sup> + c2<\/sup> = x2<\/sup> + y2<\/sup> + z2<\/sup> [\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb]<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e8\u09ed. \u09af\u09a6\u09bf x = 5a + 7b + 9c, y = b \u2013 3a \u2013 4c, z = c \u2013 2b + a \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, x + y + z = 3(a + 2b +2c).<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7,<\/p>\n\n\n\n

x = 5a + 7b + 9c
y =   b \u2013 3a  \u2013 4c
z =   c \u2013 2b  + a
\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7 =x + y + z
= (5a + 7b + 9c) + (b \u2013 3a \u2013 4c) + (c \u2013 2b + b) [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
= 5a + 7b + 9c + b \u2013 3a \u2013 4c + c \u2013 2b + a
= (5a \u2013 3a + a) + (7b + b \u2013 2b) + (9c \u2013 4c + c)
= (6a \u2013 3a) + (8b \u2013 2b) + (10c \u2013 4c)
= 3a + 6b + 6c
= 3(a + 2b + 2c)
= \u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7
\u2234 x + y + z = 3(a + 2b + 2c) [\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb]<\/p>\n\n\n\n

\u09ac\u09bf\u09df\u09cb\u0997 \u0995\u09b0 (\u09e8\u09ee \u2013 \u09e9\u09eb) :<\/mark><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e8\u09ee. 3a + 2b + c \u09a5\u09c7\u0995\u09c7 5a + 4b \u2013 2c.<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :<\/p>\n\n\n\n

   3a + 2b +  c
   5a + 4b \u2013 2c
(\u2013)  (\u2013)  (+)
<\/span>\u2013 2a \u2013 2b + 3c
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 \u2013 2a \u2013 2b + 3c<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e8\u09ef. 3ab + 6bc \u2013 2ca \u09a5\u09c7\u0995\u09c7 2ab \u2013 4bc + 8ca<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :<\/p>\n\n\n\n

      3ab + 6bc \u2013 2ca
      2ab \u2013 4bc + 8ca
   (\u2013)     (+)     (\u2013)
<\/span>   ab +10bc \u2013 10ca
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 ab +10bc \u2013 10ca<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09e6. a2<\/sup> + b2<\/sup> + c2 <\/sup>  \u09a5\u09c7\u0995\u09c7 \u2013a2<\/sup> + b2<\/sup> \u2013 c2<\/sup><\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :<\/p>\n\n\n\n

a2<\/sup> + b2<\/sup> + c2 <\/sup> <\/strong>
   \u2013a2<\/sup> + b2<\/sup> \u2013 c2<\/sup><\/strong>
  (+)  (\u2013)    (+)
<\/span>2a2 <\/sup>  +  0 + 2c2<\/sup>
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 2a2<\/sup> + 2c2<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09e7. 4ax + 5by + 6cz  \u09a5\u09c7\u0995\u09c7 6by + 3ax + 9cz<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09aa\u09b0 \u09aa\u09b0 \u09b8\u09be\u099c\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,
    4ax + 5by + 6cz <\/strong>
    3ax + 6by + 9cz<\/strong>
   (\u2013)      (\u2013)      (\u2013)      
<\/span>ax   \u2013   by  \u2013 3cz
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 ax \u2013 by \u2013 3cz<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09e8. 7x2<\/sup> + 9x + 18 \u09a5\u09c7\u0995\u09c7 5x + 9 + 8x2<\/sup><\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09aa\u09b0 \u09aa\u09b0 \u09b8\u09be\u099c\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,
7x2<\/sup> + 9x + 18
8x2<\/sup> + 5x +   9
(\u2013)    (\u2013)    (\u2013)
<\/span>\u2013 x2 <\/sup> + 4x +   9
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 (\u2013 x2 <\/sup> + 4x +   9)<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09e9. 3x3<\/sup>y2<\/sup> \u2013 5x2<\/sup>y2<\/sup> + 7xy + 2 \u09a5\u09c7\u0995\u09c7 \u2013x3<\/sup>y2<\/sup> + x2<\/sup>y2<\/sup>  <\/sub>+ 5xy + 2<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :<\/p>\n\n\n\n

3x3<\/sup>y2<\/sup> \u2013 5x2<\/sup>y2<\/sup> + 7xy + 2
\u2013 x3<\/sup>y2<\/sup> +  x2<\/sup>y2<\/sup>   <\/sub>+ 5xy + 2
(+)       (\u2013)       (\u2013)      (-)
<\/span>4x3<\/sup>y2<\/sup> \u2013 6x2<\/sup>y2<\/sup> + 2xy + 0
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 4x3<\/sup>y2<\/sup> \u2013 6x2<\/sup>y2<\/sup> + 2xy<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09ea. 4x2<\/sup> + 3y2<\/sup> + z \u09a5\u09c7\u0995\u09c7 \u2013 2y2<\/sup> + 3x2 <\/sup>\u2013 z<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :<\/p>\n\n\n\n

   4x2<\/sup> + 3y2<\/sup> + z<\/strong>
3x2<\/sup> \u2013 2y2<\/sup> \u2013 z
(\u2013)   (+)     (+)   
<\/span>x2<\/sup> + 5y2 <\/sup>+ 2z
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2  x2<\/sup> + 5y2<\/sup> + 2z<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09eb. x4<\/sup> + 2x3<\/sup> + x2<\/sup> + 4 \u09a5\u09c7\u0995\u09c7  x3<\/sup> \u2013 2x2<\/sup> + 2x + 3<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :<\/p>\n\n\n\n

x4<\/sup> + 2x3<\/sup> + x2<\/sup> + 4
x3<\/sup> \u2013 2x2<\/sup> + 2x + 3
(\u2013)    (+)     (\u2013)   (-)
<\/span>x4<\/sup> +  x3<\/sup> +  3x2  <\/sup>\u2013 2x + 1
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2  x4<\/sup> + x3<\/sup> + 3x2<\/sup> \u2013 2x + 1<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09ec. \u09af\u09a6\u09bf a = x2<\/sup> + z2<\/sup>, b = y2<\/sup> + z2<\/sup>, c = x2<\/sup> + y2<\/sup> \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, a + b \u2013 c = 2z2<\/sup><\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a = x2<\/sup> + z2<\/sup>
b = y2<\/sup> + z2<\/sup>
c = x2<\/sup> + y2<\/sup>
\u2234 \u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7 = a + b \u2013 c
=x2<\/sup> + z2<\/sup> + y2<\/sup> + z2<\/sup> \u2013 (x2<\/sup> + y2<\/sup>) [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=x2<\/sup> + z2<\/sup> + y2<\/sup> + z2<\/sup> \u2013 x2<\/sup> \u2013 y2<\/sup>
= 2z2 <\/sup>= \u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7
\u2234a + b \u2013 c = 2z2 <\/sup>[\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb]<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09ed. \u09af\u09a6\u09bf x = a + b, y = b + c, z = c + a \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, x \u2013 y + z = 2a.<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x = a + b, y = b + c, z = c + a
\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7 = x \u2013 y + z
= a + b \u2013 (b + c) + c + a
= a + b \u2013 b \u2013 c + c + a
= 2a = \u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7
\u2234x \u2013 y + z = 2a [\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb]<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09ee. \u09af\u09a6\u09bf x = a + b + c, y = a \u2013 b \u2013 c, z = b \u2013 c + a \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, x \u2013 y + z = a + 3b + c<\/strong>
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 : \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x = a + b + c, y = a \u2013 b \u2013 c, z = b \u2013 c + a
\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7 =x \u2013 y + z
= a + b + c \u2013 (a \u2013 b \u2013 c) + b \u2013 c + a
= a + b + c \u2013 a + b + c + b \u2013 c + a
= a + 3b + c
= \u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7
\u2234 x \u2013 y + z = a + 3b + c [\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb]<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09e9\u09ef. a2<\/sup>, b2<\/sup>, c2<\/sup> \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf \u09b9\u09b2\u09c7,<\/strong>
(\u0995) b2<\/sup> \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997 \u0995\u09a4?
(\u0996) a2<\/sup> \u098f\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 c2<\/sup> \u098f\u09b0 \u09a4\u09bf\u09a8\u0997\u09c1\u09a3 \u09af\u09cb\u0997 \u0995\u09b0\u0964
(\u0997) a2<\/sup> \u098f\u09b0 \u09a4\u09bf\u09a8\u0997\u09c1\u09a3 \u09a5\u09c7\u0995\u09c7 b2<\/sup> \u098f\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3 \u09ac\u09bf\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7 \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 c2<\/sup> \u098f\u09b0 \u099a\u09be\u09b0\u0997\u09c1\u09a3 \u09af\u09cb\u0997 \u0995\u09b0\u0964
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :
(\u0995) b2<\/sup> = 1 \u00d7 b2<\/sup>
\u2234 b2<\/sup> \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997 1<\/p>\n\n\n\n

(\u0996) a2<\/sup> \u098f\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3 \u09b9\u09b2\u09cb 2a2<\/sup>
c2<\/sup> \u098f\u09b0 \u09a4\u09bf\u09a8\u0997\u09c1\u09a3 \u09b9\u09b2\u09cb 3c2<\/sup>
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 2a2 <\/sup>+ 3c2<\/sup><\/p>\n\n\n\n

(\u0997) a2<\/sup> \u098f\u09b0 \u09a4\u09bf\u09a8\u0997\u09c1\u09a3 \u09b9\u09b2\u09cb 3a2<\/sup>
b2<\/sup> \u098f\u09b0 \u09a6\u09cd\u09ac\u09bf\u0997\u09c1\u09a3 \u09b9\u09b2\u09cb 2b2<\/sup>
\u2234\u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2 3a2 <\/sup>\u2013 2b2<\/sup>
c2<\/sup> \u098f\u09b0 \u099a\u09be\u09b0\u0997\u09c1\u09a3 \u09b9\u09b2\u09cb 4c2<\/sup>
\u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 4c2<\/sup> \u09af\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u09b9\u09ac\u09c7 (3a2<\/sup> \u2013 2b2<\/sup>) + 4c2<\/sup>
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 3a2<\/sup> \u2013 2b2 <\/sup>+ 4c2<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09ea\u09e6. \u098f\u0995\u099f\u09bf \u0996\u09be\u09a4\u09be\u09b0 \u09a6\u09be\u09ae x \u099f\u09be\u0995\u09be, \u098f\u0995\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae y \u099f\u09be\u0995\u09be \u098f\u09ac\u0982 \u098f\u0995\u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09a6\u09be\u09ae z \u099f\u09be\u0995\u09be \u09b9\u09b2\u09c7,<\/strong>
(\u0995) \u09e9\u099f\u09bf \u0996\u09be\u09a4\u09be \u0993 \u09e8\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09be\u09ae \u0995\u09a4?
(\u0996) \u09eb\u099f\u09bf \u0996\u09be\u09a4\u09be \u0993 \u09ee\u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09be\u09ae \u09a5\u09c7\u0995\u09c7 \u09e7\u09e6\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae \u09ac\u09be\u09a6 \u09a6\u09bf\u09b2\u09c7 \u0995\u09a4 \u09b9\u09ac\u09c7 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u0964
(\u0997) 3x \u2013 2y + 5z \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c0 \u09ac\u09cb\u099d\u09be\u09af\u09bc? y \u0993 z \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997 \u0995\u09a4? z, y \u0993 z \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997\u0997\u09c1\u09b2\u09cb\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2 \u0995\u09a4?<\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8:
(\u0995) \u09e7 \u099f\u09bf \u0996\u09be\u09a4\u09be\u09b0 \u09a6\u09be\u09aex \u099f\u09be\u0995\u09be
\u2234 \u09e9 \u099f\u09bf \u0996\u09be\u09a4\u09be\u09b0 \u09a6\u09be\u09ae 3x \u099f\u09be\u0995\u09be
\u09e7 \u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae y \u099f\u09be\u0995\u09be
\u2234 \u09e8 \u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae 2y \u099f\u09be\u0995\u09be
\u2234 \u09e9 \u099f\u09bf \u0996\u09be\u09a4\u09be \u0993 \u09e8\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09be\u09ae (3x + 2y) \u099f\u09be\u0995\u09be (Ans.)<\/p>\n\n\n\n

(\u0996) \u09e7 \u099f\u09bf \u0996\u09be\u09a4\u09be\u09b0 \u09a6\u09be\u09ae x \u099f\u09be\u0995\u09be
\u2234 \u09eb \u099f\u09bf \u0996\u09be\u09a4\u09be\u09b0 \u09a6\u09be\u09ae 5x \u099f\u09be\u0995\u09be
\u09e7 \u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09a6\u09be\u09ae z \u099f\u09be\u0995\u09be
\u2234 \u09ee \u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09a6\u09be\u09ae 8z \u099f\u09be\u0995\u09be
\u2234 \u09eb \u099f\u09bf \u0996\u09be\u09a4\u09be \u0993 \u09ee\u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09be\u09ae (5x + 8z) \u099f\u09be\u0995\u09be
\u09e7\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae y \u099f\u09be\u0995\u09be
\u2234 \u09e7\u09e6\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae 10y \u099f\u09be\u0995\u09be
\u09eb\u099f\u09bf \u0996\u09be\u09a4\u09be \u0993 \u09ee\u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09be\u09ae \u09a5\u09c7\u0995\u09c7
\u09e7\u09e6\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae \u09ac\u09be\u09a6 \u09a6\u09bf\u09b2\u09c7 \u09b9\u09ac\u09c7 {(5x + 8z) \u2013 10y}<\/p>\n\n\n\n

(\u0997) 3x \u2013 2y + 5z
\u098f\u0996\u09be\u09a8\u09c7, 3x \u09b9\u09b2\u09cb \u09e9\u099f\u09bf \u0996\u09be\u09a4\u09be\u09b0 \u09a6\u09be\u09ae
2y \u09b9\u09b2\u09cb \u09e8\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae
5z \u09b9\u09b2\u09cb \u09eb\u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09a6\u09be\u09ae
\u2234 3x \u2013 2y + 5z   \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ac\u09cb\u099d\u09be\u09af\u09bc,
\u09e9\u099f\u09bf \u0996\u09be\u09a4\u09be \u0993 \u09e8\u099f\u09bf \u0995\u09b2\u09ae\u09c7\u09b0 \u09a6\u09be\u09ae\u09c7\u09b0 \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09eb\u099f\u09bf \u09aa\u09c7\u09a8\u09cd\u09b8\u09bf\u09b2\u09c7\u09b0 \u09a6\u09be\u09ae\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2\u0964 (Ans.)
3x \u2013 2y + 5z \u098f
x \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997 \u09e9
y \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997 \u2013 \u09e8
z \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997 \u09eb
(Ans.)
\u2234x, y, z \u098f\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997\u0997\u09c1\u09b2\u09cb\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2
= 3 \u00d7 (\u2013 2) \u00d7 5
= \u2013 30 (Ans.)<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09ea\u09e7. 5x2<\/sup> + xy + 3y2<\/sup>, x2<\/sup> \u2013 8xy, y2<\/sup> \u2013 x2<\/sup> + 10xy \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf \u09b9\u09b2\u09c7,<\/strong>
(\u0995) \u09aa\u09cd\u09b0\u09a5\u09ae \u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09b0 \u09aa\u09a6\u09b8\u0982\u0996\u09cd\u09af\u09be \u0995\u09af\u09bc\u099f\u09bf \u098f\u09ac\u0982 \u0995\u09c0 \u0995\u09c0?
(\u0996) \u09b0\u09be\u09b6\u09bf \u09a4\u09bf\u09a8\u099f\u09bf \u09af\u09cb\u0997 \u0995\u09b0\u0964 \u09af\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 xy \u098f\u09b0 \u09b8\u09b9\u0997 \u0995\u09a4?
(\u0997) (5x2<\/sup> + xy + 3y2<\/sup>) \u2013 (x2<\/sup> \u2013 8xy) \u2013 (y2<\/sup> \u2013 x2<\/sup> + 10xy) \u09b8\u09b0\u09b2 \u0995\u09b0\u09c7 \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0; \u09af\u0996\u09a8 x = 2 \u098f\u09ac\u0982 y = 1.
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :
(\u0995) \u09e7\u09ae \u09b0\u09be\u09b6\u09bf = 5x2<\/sup> + xy + 3y2<\/sup>
\u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09b0 \u09aa\u09a6\u09b8\u0982\u0996\u09cd\u09af\u09be \u09e9\u099f\u09bf (Ans.)
\u09e7\u09ae \u09aa\u09a6 = 5x2<\/sup>, \u09e8\u09af\u09bc \u09aa\u09a6 = xy, \u09e9\u09af\u09bc \u09aa\u09a6 = 3y2<\/sup> (Ans.)
(\u0996) \u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6\u0997\u09c1\u09b2\u09cb \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u09ac-\u09b8\u09cd\u09ac \u099a\u09bf\u09b9\u09cd\u09a8\u09b8\u09b9 \u09a8\u09bf\u099a\u09c7 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09c7 \u09aa\u09be\u0987;
5x2 <\/sup> +     xy + 3y2<\/sup>
x2<\/sup>  \u2013    8xy
\u2013 x2<\/sup>  + 10xy +  y2<\/sup>
<\/span>5x2<\/sup>  + 3xy   + 4y2  <\/sup>
\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09af\u09cb\u0997\u09ab\u09b2 5x2<\/sup>  + 3xy  + 4y2<\/sup>  \u098f\u09ac\u0982 xy \u098f\u09b0 \u09b8\u09b9\u0997 \u09e9 (Ans.)<\/p>\n\n\n\n

(\u0997) (5x2<\/sup> + xy + 3y2<\/sup>) \u2013 (x2<\/sup> \u2013 8xy) \u2013 (y2<\/sup> \u2013 x2<\/sup> + 10xy)
= 5x2<\/sup> + xy + 3y2<\/sup> \u2013 x2<\/sup> + 8xy \u2013 y2<\/sup> + x2<\/sup> \u2013 10xy
= (5x2<\/sup> \u2013 x2<\/sup> + x2<\/sup>) + (xy + 8xy \u2013 10xy) + (3y2<\/sup> \u2013 y2<\/sup> )
= 5x2<\/sup> \u2013 xy + 2y2<\/sup>
= 5 \u00d7 (2)2<\/sup> \u2013 2 \u00d71 + 2.(1)2<\/sup>   [Q x = 2, y = 1 ]
= 5 \u00d7 4 \u2013 2 + 2\u09e8
= 20 \u2013 2 + 2
= 20 (Ans.)<\/p>\n\n\n\n

 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u0983 \u09ea\u09e8. x = (a + b)2<\/sup>, y = a2<\/sup> + 2ab + b2<\/sup>, \u098f\u09ac\u0982 z = a2<\/sup> + b2<\/sup> \u2013 2ab<\/strong><\/p>\n\n\n\n

(\u0995) z \u09aa\u09a6\u0997\u09c1\u09b2\u09cb\u09b0 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997\u0997\u09c1\u09b2\u09cb\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u0964
(\u0996)  y + z \u098f\u09ac\u0982 y \u2013 z \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u0964
(\u0997) a = 3 \u098f\u09ac\u0982 b = \u2013 2  \u09b9\u09b2\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0 \u09af\u09c7, x = y
\u09b8\u09ae\u09be\u09a7\u09be\u09a8 :
(\u0995) \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, z = a2<\/sup> + b2<\/sup> \u2013 2ab
\u09b0\u09be\u09b6\u09bf\u099f\u09bf\u09a4\u09c7 a2<\/sup>, b2<\/sup> \u0993 ab  \u098f\u09b0 \u09b8\u09b9\u0997 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \u09e7, \u09e7 \u0993 \u2013 \u09e8
\u2234 \u09b8\u09be\u0982\u0996\u09cd\u09af\u09bf\u0995 \u09b8\u09b9\u0997\u0997\u09c1\u09b2\u09cb\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 = 1 + 1 \u2013 2
= \u09e6 (Ans.)<\/p>\n\n\n\n

(\u0996) \u098f\u0996\u09be\u09a8\u09c7,
y = a2<\/sup> + 2ab + b2<\/sup>
\u098f\u09ac\u0982 z = a2<\/sup> + b2<\/sup> \u2013 2ab
\u2234 y + z = (a2<\/sup> + 2ab + b2<\/sup>) + (a2<\/sup> + b2<\/sup> \u2013 2ab)<\/p>\n\n\n\n

= a2<\/sup> + 2ab + b2<\/sup> + a2<\/sup> + b2<\/sup> \u2013 2ab
= 2a2<\/sup> + 2b2<\/sup>
= 2(a2<\/sup> + b2<\/sup>) (Ans.)<\/strong><\/p>\n\n\n\n

\u098f\u09ac\u0982 y \u2013 z = (a2<\/sup> + 2ab + b2<\/sup>) \u2013 (a2<\/sup> + b2<\/sup> \u2013 2ab)
= a2<\/sup> + 2ab + b2<\/sup> \u2013 a2<\/sup> \u2013 b2<\/sup> + 2ab
= 4ab (Ans.)<\/strong><\/p>\n\n\n\n

(\u0997) \u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a = 3 \u098f\u09ac\u0982 b = \u2013 2
\u2234 x = (a + b)2<\/sup>
= {3 + (- 2)}2<\/sup>
= (3 \u2013 2)2<\/sup>
=12<\/sup> = 1
\u098f\u09ac\u0982 y = a2<\/sup> + 2ab + b2<\/sup> = 32<\/sup> + 2 \u00d7 3 \u00d7 (- 2) + (- 2)2<\/sup>
= 9 \u2013 12 + 4
= 13 \u2013 12
=1
\u2234 x = y (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n","protected":false},"excerpt":{"rendered":"

\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u09ec\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Six (06) Math Book Solution | Chapter 04 : Algebraic Expressions | Online Solution \u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 : \u09b8\u09a6\u09c3\u09b6 \u0993 \u09ac\u09bf\u09b8\u09a6\u09c3\u09b6 \u09aa\u09a6 \u0993 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf\u09b0\u09af\u09cb\u0997 \u09ac\u09bf\u09af\u09bc\u09cb\u0997 \u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 \u098f\u09b0 \u09b8\u0995\u09b2 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u0989\u09a4\u09cd\u09a4\u09b0 \u098f\u0996\u09be\u09a8\u09c7 \u09b0\u09df\u09c7\u099b\u09c7\u0964 \u09ec\u09b7\u09cd\u09a0 […]<\/p>\n","protected":false},"author":1,"featured_media":3760,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[28],"tags":[29,30],"class_list":["post-4149","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-six-06","tag-class-6","tag-class-six"],"yoast_head":"\n\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983\u00a0\u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 | \u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD<\/title>\n<meta name=\"description\" content=\"\u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Six (06) Math Book.. Solution ..Chapter 04 : Algebraic Expressions all solution \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8..\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983\u00a0\u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 | \u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD\" \/>\n<meta property=\"og:description\" content=\"\u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Six (06) Math Book.. 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Solution ..Chapter 04 : Algebraic Expressions all solution \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8..","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/","og_locale":"en_US","og_type":"article","og_title":"\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983\u00a0\u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 | \u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD","og_description":"\u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Six (06) Math Book.. Solution ..Chapter 04 : Algebraic Expressions all solution \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8..","og_url":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/","og_site_name":"Study Zone BD","article_publisher":"https:\/\/www.facebook.com\/studyzonebdcom\/","article_author":"https:\/\/www.facebook.com\/studyzonebdcom\/","article_published_time":"2022-09-23T18:51:57+00:00","article_modified_time":"2022-09-23T19:30:55+00:00","og_image":[{"width":1200,"height":675,"url":"https:\/\/www.studyzonebd.com\/math\/wp-content\/uploads\/2022\/09\/Class-six-6-math-book-solution-chapter-1-lesson-1.1.jpg","type":"image\/jpeg"}],"author":"StudyZone BD","twitter_card":"summary_large_image","twitter_creator":"@StudyZoneBD_com","twitter_site":"@StudyZoneBD_com","twitter_misc":{"Written by":"StudyZone BD","Est. reading time":"13 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/#article","isPartOf":{"@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/"},"author":{"name":"StudyZone BD","@id":"https:\/\/www.studyzonebd.com\/math\/#\/schema\/person\/eb47b9e07c0f27fa4d114357c2eda1e2"},"headline":"\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983\u00a0\u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 | \u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf","datePublished":"2022-09-23T18:51:57+00:00","dateModified":"2022-09-23T19:30:55+00:00","mainEntityOfPage":{"@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/"},"wordCount":1832,"publisher":{"@id":"https:\/\/www.studyzonebd.com\/math\/#organization"},"image":{"@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/#primaryimage"},"thumbnailUrl":"https:\/\/www.studyzonebd.com\/math\/wp-content\/uploads\/2022\/09\/Class-six-6-math-book-solution-chapter-1-lesson-1.1.jpg","keywords":["Class 6","Class Six"],"articleSection":["Class Six (06)"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/","url":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/","name":"\u0985\u09a7\u09cd\u09af\u09be\u09df \u09ea\u09b0\u09cd\u09a5\u0983\u00a0\u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e9 | \u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD","isPartOf":{"@id":"https:\/\/www.studyzonebd.com\/math\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/#primaryimage"},"image":{"@id":"https:\/\/www.studyzonebd.com\/math\/class-six-chapter-04-lesson-4-3\/#primaryimage"},"thumbnailUrl":"https:\/\/www.studyzonebd.com\/math\/wp-content\/uploads\/2022\/09\/Class-six-6-math-book-solution-chapter-1-lesson-1.1.jpg","datePublished":"2022-09-23T18:51:57+00:00","dateModified":"2022-09-23T19:30:55+00:00","description":"\u09b7\u09b7\u09cd\u09a0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Six (06) Math Book.. 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