{"id":4959,"date":"2022-09-28T20:32:28","date_gmt":"2022-09-28T20:32:28","guid":{"rendered":"https:\/\/www.studyzonebd.com\/math\/?p=4959"},"modified":"2022-09-28T20:38:08","modified_gmt":"2022-09-28T20:38:08","slug":"class-8-chapter-4-lesson-4-1","status":"publish","type":"post","link":"https:\/\/www.studyzonebd.com\/math\/class-8-chapter-4-lesson-4-1\/","title":{"rendered":"\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e7 | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf"},"content":{"rendered":"\n

\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u09ee\u09ae \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 Eight (08) Math <\/a>Book Solution | Chapter <\/a>04 : Algebraic formulas and applications| Class 8 math book Online Solution in Bangla (BD)<\/p>\n\n\n\n

\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997| \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e7: \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 – PDF<\/a><\/h4>\n\n\n\n

\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e7 \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 \u09ee\u09ae \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

\u09ee\u09ae \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.\u09e7 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/strong><\/span><\/h4>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e7\u0983 \u09b8\u09c1\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u0997\u09c1\u09b2\u09cb\u09b0 \u09ac\u09b0\u09cd\u0997 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

(\u0995) 5a + 7b    (\u0996) 6x + 3       (\u0997) 7 p + 2q<\/p>\n\n\n\n

(\u0998) ax – by      (\u0999) x + xy 3    (\u099a) 11a -12b<\/p>\n\n\n\n

(\u099b) 6×2 y -5xy 2         (\u099c) – x – y       (\u099d) – xyz – abc<\/p>\n\n\n\n

(\u099e) a2x3 – b2 y4       (\u099f) 108           (\u09a0) 606<\/p>\n\n\n\n

(\u09a1) 597           (\u09a2) a – b + c    (\u09a3) ax + b + 2<\/p>\n\n\n\n

(\u09a4) xy + yz -zx           (\u09a5) 3 p + 2q – 5r        (\u09a6) x2<\/sup> – y2<\/sup> – z2<\/sup><\/a><\/p>\n\n\n\n

(\u0995) 5a + 7b<\/strong><\/p>\n\n\n\n

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

5a + 7b \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

=(5a+7b)2<\/sup><\/p>\n\n\n\n

=(5a)2<\/sup>+2*(5a)*(7b)+(7b)2<\/sup><\/p>\n\n\n\n

=25a2<\/sup>+70ab+49b2<\/sup><\/p>\n\n\n\n

(\u0996) 6x + 3<\/strong><\/p>\n\n\n\n

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

6x + 3 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (6x + 3)2<\/sup><\/p>\n\n\n\n

= (6x)2<\/sup> + 2 * (6x) * (3) + (3)2<\/sup><\/p>\n\n\n\n

= 36 x 2 + 36 x + 9<\/p>\n\n\n\n

(\u0997) 7 p + 2q<\/strong><\/p>\n\n\n\n

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

7p + 2q \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (7p + 2q)2<\/sup><\/p>\n\n\n\n

= (7p)2<\/sup> + 2 * (7 p) * (2q) + (2q)2<\/sup><\/p>\n\n\n\n

= 49p2 <\/sup>+ 28pq + 4q2<\/sup><\/p>\n\n\n\n

(\u0998) ax – by<\/strong><\/p>\n\n\n\n

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

ax + by \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (ax -by)2<\/sup><\/p>\n\n\n\n

= (ax)2<\/sup> -2 * (ax) * (by) + (by)2<\/sup><\/p>\n\n\n\n

= a2<\/sup> x2<\/sup> -2abxy + b2<\/sup> y 2<\/sup><\/p>\n\n\n\n

(\u0999) x3<\/sup> + xy<\/strong><\/p>\n\n\n\n

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

x3<\/sup> + xy \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (x3<\/sup> + xy)2<\/sup><\/p>\n\n\n\n

= (x3<\/sup> )2<\/sup> + 2 * (x3<\/sup> ) * (xy) + (xy)2<\/sup><\/p>\n\n\n\n

= x 6<\/sup> + 2x4<\/sup> y + x 2<\/sup> y 2<\/sup><\/p>\n\n\n\n

(\u099a) 11a -12b<\/strong><\/p>\n\n\n\n

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

11a -12b \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (11a -12b)2<\/sup><\/p>\n\n\n\n

= (11a)2<\/sup>– 2* (11a) * (12b) + (12b)2<\/sup><\/p>\n\n\n\n

= 121a2<\/sup> + 264 ab + 144 b2<\/sup><\/p>\n\n\n\n

(\u099b) 6x2<\/sup> y – 5xy2<\/sup><\/strong><\/p>\n\n\n\n

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

6x2<\/sup> y – 5xy2<\/sup> \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (6x2<\/sup> y – 5xy 2<\/sup> )2<\/sup><\/p>\n\n\n\n

= (6x2<\/sup> y)2<\/sup>– 2*(6x2<\/sup> y)*(5xy2<\/sup> ) + (5xy2<\/sup> )2<\/sup><\/p>\n\n\n\n

= 36 x 4<\/sup> y 2<\/sup> – 60 x3<\/sup> y 3<\/sup> + 25 x 2<\/sup> y 4<\/sup><\/p>\n\n\n\n

(\u099c) – x – y<\/strong><\/p>\n\n\n\n

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

-x – y \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (-x – y)2<\/sup><\/p>\n\n\n\n

= {-(x + y)}2<\/sup><\/p>\n\n\n\n

= (x + y)2<\/sup><\/p>\n\n\n\n

= y2<\/sup> + 2xy + y2<\/sup><\/p>\n\n\n\n

(\u099d) \u2013xyz- acb<\/strong><\/p>\n\n\n\n

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

-xyz- abc \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (-xyz – abc)2<\/sup><\/p>\n\n\n\n

= {-(xyz + abc)}2<\/sup><\/p>\n\n\n\n

= (xyz + abc)2<\/sup><\/p>\n\n\n\n

= (xyz)2<\/sup> + 2* (xyz)* (abc) + (abc)2<\/sup><\/p>\n\n\n\n

= x2<\/sup> y 2<\/sup> z2<\/sup> + 2xyzabc + a2<\/sup>b2<\/sup>c2<\/sup><\/p>\n\n\n\n

 (\u099e) a2<\/sup>x3<\/sup> – b2<\/sup> y4<\/sup><\/strong><\/p>\n\n\n\n

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

a2<\/sup>x3<\/sup> – b2<\/sup> y4<\/sup> \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (a2 x3<\/sup> – b2 y4<\/sup> )2<\/sup><\/p>\n\n\n\n

= (a2<\/sup>x3<\/sup>)2<\/sup> -2*(a2<\/sup>x3<\/sup>)*(b2<\/sup> y4<\/sup> ) +(b2<\/sup> y4<\/sup> )2<\/sup><\/p>\n\n\n\n

= a4<\/sup> x6<\/sup> – 2a2<\/sup>b2<\/sup> x3<\/sup> y4<\/sup> + b4<\/sup> y8<\/sup><\/p>\n\n\n\n

(\u099f) 108<\/strong><\/p>\n\n\n\n

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

108 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (108)2<\/sup><\/p>\n\n\n\n

= (100 + 8)2<\/sup><\/p>\n\n\n\n

= (100)2<\/sup> + 2 \uf0b4 (100) \uf0b4 (8) \uf02b (8)2<\/sup><\/p>\n\n\n\n

= 10000 +1600 + 64<\/p>\n\n\n\n

= 11664<\/p>\n\n\n\n

(\u09a0) 606<\/strong><\/p>\n\n\n\n

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

606 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (606)2<\/sup><\/p>\n\n\n\n

= (600 + 6)2<\/sup><\/p>\n\n\n\n

= (600)2<\/sup> + 2*(600)* (6) + (6)2<\/sup><\/p>\n\n\n\n

= 360000 +7200 + 36<\/p>\n\n\n\n

= 367236<\/p>\n\n\n\n

(\u09a1) 597<\/strong><\/p>\n\n\n\n

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

597 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (597)2<\/sup><\/p>\n\n\n\n

= (600 -3)2<\/sup><\/p>\n\n\n\n

= (600)2<\/sup> – 2* (600) * (3) + (3)2<\/sup><\/p>\n\n\n\n

= 360000 – 36000 + 9<\/p>\n\n\n\n

= 360009 – 3600<\/p>\n\n\n\n

= 356409<\/p>\n\n\n\n

(\u09a2) a – b + c<\/strong><\/p>\n\n\n\n

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

a – b +c \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (a – b + c)2<\/sup><\/p>\n\n\n\n

= {(a – b) + c}2<\/sup><\/p>\n\n\n\n

= (a -b)2<\/sup> + 2*(a – b)* (c) + (c)2<\/sup><\/p>\n\n\n\n

= a2 <\/sup>– 2ab + b2<\/sup> + 2ac – 2bc +c2<\/sup><\/p>\n\n\n\n

= a2<\/sup> + b2<\/sup> + c2<\/sup> – 2ab – 2bc + 2ac<\/p>\n\n\n\n

(\u09a3) ax + b + 2<\/strong><\/p>\n\n\n\n

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

ax + b + 2 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (ax + b + 2)2<\/sup><\/p>\n\n\n\n

= {(ax + b) + 2}2<\/sup><\/p>\n\n\n\n

= (ax + b)2<\/sup> + 2* (ax + b)* (2) + (2)2<\/sup><\/p>\n\n\n\n

= a2<\/sup>x2<\/sup> + 2abx + b2<\/sup> + 4ax + 4b + 4<\/p>\n\n\n\n

= a2<\/sup> x2<\/sup> + b2<\/sup> + 2abx + 4b + 4ax + 4<\/p>\n\n\n\n

(\u09a4) xy + yz + zx<\/strong><\/p>\n\n\n\n

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

xy + yz – zx \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (xy + yz + zx)2<\/sup><\/p>\n\n\n\n

= {xy + ( yz – zx)}2<\/sup><\/p>\n\n\n\n

=(xy)2<\/sup> +2*(xy)*(yz-zx)+(yz-zx)2<\/sup><\/p>\n\n\n\n

= x2<\/sup> y2<\/sup> + 2xy2 z – 2x2<\/sup> yz + ( yz)2<\/sup> – 2( yz)(zx) – (zx)2<\/sup><\/p>\n\n\n\n

= x2<\/sup>y2<\/sup> + y2<\/sup>z2<\/sup> +z2<\/sup>x2<\/sup> -2x2<\/sup>yz+2xy2<\/sup>z-2xyz2<\/sup><\/p>\n\n\n\n

(\u09a5) 3 p + 2q – 5r<\/strong><\/p>\n\n\n\n

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

3p + 2q – 5r \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= (3 p + 2q – 5r)2<\/sup><\/p>\n\n\n\n

= {3 p + (2q – 5r)}2<\/sup><\/p>\n\n\n\n

=(3p)2<\/sup> +2*(3p)*(2q-5r)+(2q\uf02d5r)2<\/sup><\/p>\n\n\n\n

=9p2<\/sup> +12pq-30qr+(2q)2<\/sup> -2(2q)(5r)+(5r)2<\/sup><\/p>\n\n\n\n

= 9p2<\/sup> +12pq-30qr + 4q2<\/sup> -20qr +5r2<\/sup><\/p>\n\n\n\n

= 9p2<\/sup> +4q2<\/sup> +5r2<\/sup> +12pq-30qr -20qr<\/p>\n\n\n\n

(\u09a6) x2<\/sup> – y2<\/sup> – z2<\/sup><\/strong><\/p>\n\n\n\n

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

x2<\/sup> -y2<\/sup> -z2<\/sup> \u098f\u09b0 \u09ac\u09b0\u09cd\u0997<\/p>\n\n\n\n

= ( x2<\/sup> – y2<\/sup> – z2<\/sup> )2<\/sup><\/p>\n\n\n\n

= {( x2<\/sup> – y2<\/sup> ) – z2<\/sup>}2<\/p>\n\n\n\n

= (x2<\/sup> – y2<\/sup> )2<\/sup> \u2013 2*(x2<\/sup> – y2<\/sup> )*(z2<\/sup> ) + (z2<\/sup> )2<\/sup><\/p>\n\n\n\n

= x4<\/sup> – 2x2<\/sup> y2<\/sup> + y4<\/sup> – 2x2<\/sup> z2<\/sup> + 2x2<\/sup> z2<\/sup> + z4<\/sup><\/p>\n\n\n\n

= x4 <\/sup>+ y4<\/sup> + z4<\/sup> – 2x2<\/sup> y2<\/sup> + 2y2<\/sup>z2<\/sup> – 2x2<\/sup>z2<\/sup><\/p>\n\n\n\n

(\u09a7) 7a2<\/sup> + 8b2<\/sup> – 5c2<\/sup><\/strong><\/p>\n\n\n\n

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

7a2<\/sup> + 8b2<\/sup> – 5c2<\/sup> \u098f\u09b0 \u09ac\u0997\udbc0\udded<\/p>\n\n\n\n

= (7a2<\/sup> + 8b2<\/sup> – 5c2<\/sup> )2<\/sup><\/p>\n\n\n\n

= {7a2<\/sup> + (8b2<\/sup> – 5c2<\/sup> )}2<\/sup><\/p>\n\n\n\n

= (7a2<\/sup>)2<\/sup> +2(7a2<\/sup>)(8b2<\/sup> -5c2<\/sup>)+(8b2<\/sup> -5c2<\/sup>)2<\/sup><\/p>\n\n\n\n

= 49a 4<\/sup> +112a 2<\/sup>b 2<\/sup> – 70a 2<\/sup>c 2<\/sup> + (8b 2<\/sup> ) 2<\/sup> – 2(8b 2<\/sup> )(5c 2<\/sup> ) – (5c 2<\/sup> ) 2<\/sup><\/p>\n\n\n\n

= 49a4<\/sup> +112a2<\/sup>b2<\/sup> – 70a2<\/sup>c2<\/sup> + 64b4 <\/sup>-80b2<\/sup>c2<\/sup> + 25c4<\/sup><\/p>\n\n\n\n

= 49a4<\/sup> + 64b4<\/sup> +25c4<\/sup> +112a2<\/sup>b2<\/sup> -80b2<\/sup>c2<\/sup> – 70a2<\/sup>c2<\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e8\u0983 \u09b8\u09b0\u09b2 \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

\u0995. (x+y)2<\/sup>+2(x+y)(x-y)+(x-y)2<\/sup><\/p>\n\n\n\n

(\u0996) (2a+3b)2<\/sup> -2(2a +3b)(3b-a) +(3b-a)2<\/sup><\/p>\n\n\n\n

(\u0997) (3x2<\/sup> +7y2<\/sup>)2<\/sup> +2(3x2<\/sup> +7y2<\/sup>)(3x2<\/sup> -7y2<\/sup>)+(3x2<\/sup> -7y2<\/sup>)2<\/sup><\/p>\n\n\n\n

(\u0998) (8x + y)2<\/sup> -(16x +2y)(5x + y)+(5x+ y)2<\/sup><\/p>\n\n\n\n

(\u0999) (5x2<\/sup> -3x -2)2<\/sup> +(2+5x2<\/sup> -3x)2<\/sup> -2(5x2<\/sup> -3x+ 2)(2+5x2<\/sup> -3x)<\/p>\n\n\n\n

\u0995. (x+y)2<\/sup>+2(x+y)(x-y)+(x-y)<\/strong>2<\/strong><\/sup><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, x + y = a<\/p>\n\n\n\n

\u098f\u09ac\u0982 x – y = b<\/p>\n\n\n\n

\u2234 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a2<\/sup>+2ab+b2<\/sup><\/p>\n\n\n\n

                        <\/sup>=(a+b)2<\/sup><\/p>\n\n\n\n

                        =(x+y+x-y)2<\/sup> [a \u0993 b \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987]<\/p>\n\n\n\n

                        =(2x)2<\/sup><\/p>\n\n\n\n

                        <\/sup>=4x2<\/sup><\/p>\n\n\n\n

(\u0996) (2a+3b)2<\/sup> -2(2a +3b)(3b-a) +(3b-a)2<\/sup><\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 2a+3b=x<\/p>\n\n\n\n

\u098f\u09ac\u0982, 3b-a=y<\/p>\n\n\n\n

\u2234 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf=x2<\/sup>-2xy+y2<\/sup><\/p>\n\n\n\n

                         <\/sup>=(x-y)2<\/sup><\/p>\n\n\n\n

                         <\/sup>={(2a+3b)-(3b-a)}2<\/sup>  [ x,y \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09be\u0987]<\/p>\n\n\n\n

                        =(2a+3b-3b+a)2<\/sup><\/p>\n\n\n\n

                         <\/sup>=(3a)2<\/sup><\/p>\n\n\n\n

                        =9a2<\/sup><\/p>\n\n\n\n

(\u0997) (3x2<\/sup> +7y2<\/sup>)2<\/sup> +2(3x2<\/sup> +7y2<\/sup>)(3x2<\/sup> -7y2<\/sup>)+(3x2<\/sup> +7y2<\/sup>)2<\/sup><\/strong><\/p>\n\n\n\n

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

(3x2<\/sup> +7y2<\/sup>)2<\/sup> +2(3x2<\/sup> +7y2<\/sup>)(3x2<\/sup> -7y2<\/sup>)+(3x2<\/sup> -7y2<\/sup>)2<\/sup><\/p>\n\n\n\n

={(3x2<\/sup> +7y2<\/sup>)+ (3x2<\/sup> -7y2<\/sup>)}2<\/sup><\/p>\n\n\n\n

=(3x2<\/sup> +7y2<\/sup>+ 3x2<\/sup> -7y2<\/sup>)2<\/sup><\/p>\n\n\n\n

=(6x2<\/sup>)2<\/sup><\/p>\n\n\n\n

=36x4<\/sup><\/p>\n\n\n\n

(\u0998) (8x + y)2<\/sup> -(16x +2y)(5x + y)+(5x+ y)2<\/sup><\/strong><\/p>\n\n\n\n

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

(8x + y)2<\/sup> -(16x +2y)(5x + y)+(5x+ y)2<\/sup><\/p>\n\n\n\n

=(8x + y)2<\/sup> -2(8x +y)(5x + y)+(5x+ y)2<\/sup><\/p>\n\n\n\n

={(8x+y)-(5x+y)}2<\/sup><\/p>\n\n\n\n

=(8x+y-5x-y)2<\/sup><\/p>\n\n\n\n

=(3x)2<\/sup><\/p>\n\n\n\n

=9x2<\/sup><\/p>\n\n\n\n

(\u0999) (5x2<\/sup> -3x -2)2<\/sup> +(2+5x2<\/sup> -3x)2<\/sup> -2(5x2<\/sup> -3x+ 2)(2+5x2<\/sup> -3x)<\/strong><\/p>\n\n\n\n

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

(5x2<\/sup> -3x -2)2<\/sup> +(2+5x2<\/sup> -3x)2<\/sup> -2(5x2<\/sup> -3x+ 2)(2+5x2<\/sup> -3x)<\/p>\n\n\n\n

={(5x2<\/sup> -3x -2) -(2+5x2<\/sup> -3x)}2<\/sup><\/p>\n\n\n\n

=(5x2<\/sup> -3x -2 -2-5x2<\/sup> +3x)2<\/sup><\/p>\n\n\n\n

=(-4)2<\/sup><\/p>\n\n\n\n

=16<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e9\u0983 \u09b8\u09c1\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7 \u0997\u09c1\u09a8\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

(\u0995) (x + 7)(x – 7)                    (\u0996) (5x +13)(5x -13)<\/p>\n\n\n\n

(\u0997) (xy + yz)(xy – yz)             (\u0998) (ax + b)(ax – b)<\/p>\n\n\n\n

(\u0999) (a + 3)(a + 4)                  (\u099a) (ax + 3)(ax + 4)<\/p>\n\n\n\n

(\u099b) (6x +17)(6x -13)              (\u099c) (a2<\/sup> + b2<\/sup> )(a2<\/sup> – b2<\/sup> )(a4<\/sup> + b4<\/sup> )<\/p>\n\n\n\n

(\u099d) (ax – by + cz)(ax + by – cz)         (\u099e) (3a -10)(3a – 5)<\/p>\n\n\n\n

(\u099f) (5a + 2b – 3c)(5a + 2b +3c)       (\u09a0) (ax + by + 5)(ax + by + 3)<\/p>\n\n\n\n

(\u0995) (x + 7)(x – 7)   <\/strong>    <\/p>\n\n\n\n

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

(x + 7)(x – 7)<\/p>\n\n\n\n

=x2<\/sup>-72<\/sup><\/p>\n\n\n\n

=x2<\/sup>-49<\/p>\n\n\n\n

 (\u0996) (5x +13)(5x -13)<\/strong><\/p>\n\n\n\n

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

(5x +13)(5x -13)<\/p>\n\n\n\n

=(5x)2<\/sup> \u2013(13)2<\/sup><\/p>\n\n\n\n

=25x2<\/sup>-169<\/p>\n\n\n\n

(\u0997) (xy + yz)(xy – yz)<\/strong><\/p>\n\n\n\n

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

(xy + yz)(xy – yz)<\/p>\n\n\n\n

=(xy)2<\/sup> \u2013 (yz)2<\/sup><\/p>\n\n\n\n

=x2<\/sup> y2<\/sup>-y2<\/sup> z2<\/sup><\/p>\n\n\n\n

(\u0998) (ax + b)(ax – b)<\/strong><\/p>\n\n\n\n

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

(ax + b)(ax – b)<\/p>\n\n\n\n

=(ax)2<\/sup> \u2013(b)2<\/sup><\/p>\n\n\n\n

=a2<\/sup> x2<\/sup>-b2<\/sup><\/p>\n\n\n\n

(\u0999) (a + 3)(a – 4)<\/strong><\/p>\n\n\n\n

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

(a + 3)(a +4)<\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, (x+a)(x+b)=x2<\/sup>+(a+b)x+ab<\/p>\n\n\n\n

\u2234(a + 3)(a +4)<\/p>\n\n\n\n

=a2<\/sup>+(3+4)a+(3)(4)<\/p>\n\n\n\n

=a2<\/sup>+7a+12<\/p>\n\n\n\n

(\u099a) (ax + 3)(ax + 4)<\/strong><\/p>\n\n\n\n

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

(ax + 3)(ax + 4)<\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, (x+a)(x+b)=x2<\/sup>+(a+b)x+ab<\/p>\n\n\n\n

\u2234(ax + 3)(ax + 4)<\/p>\n\n\n\n

=(ax)2<\/sup>+(3+4)ax+(3)(4)<\/p>\n\n\n\n

=a2<\/sup>x2<\/sup>+7ax+12<\/p>\n\n\n\n

(\u099b) (6x +17)(6x -13)<\/strong> <\/p>\n\n\n\n

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

(6x +17)(6x -13)<\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/p>\n\n\n\n

(x+a)(x-b)=x2<\/sup>+(a-b)x-ab<\/p>\n\n\n\n

\u2234(6x +17)(6x -13)<\/p>\n\n\n\n

= (6x)2<\/sup> + (17 -13)6x – (17)(13)<\/p>\n\n\n\n

= 36x2<\/sup> + 4x -221<\/p>\n\n\n\n

(\u099c) (a2<\/sup> + b2<\/sup> )(a2<\/sup> – b2<\/sup> )(a4<\/sup> + b4<\/sup> )<\/strong><\/p>\n\n\n\n

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

(a2<\/sup> + b2<\/sup> )(a2<\/sup> – b2<\/sup> )(a4<\/sup> + b4<\/sup> )<\/p>\n\n\n\n

={(a2<\/sup> )2<\/sup>– (b2<\/sup> )2<\/sup>}(a4<\/sup> + b4<\/sup> )<\/p>\n\n\n\n

=(a4<\/sup> – b4<\/sup> ) (a4<\/sup> + b4<\/sup> )<\/p>\n\n\n\n

=(a4<\/sup>)2<\/sup> \u2013 (b4<\/sup>)2<\/sup><\/p>\n\n\n\n

=a8<\/sup>-b8<\/sup><\/p>\n\n\n\n

(\u099d) (ax – by + cz)(ax + by – cz)<\/strong><\/p>\n\n\n\n

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

(ax – by + cz)(ax + by – cz)<\/p>\n\n\n\n

={(ax \u2013 (by – cz)}{(ax) + (by – cz)}<\/p>\n\n\n\n

= (ax)2<\/sup> \u2013 (by – cz)2<\/sup><\/p>\n\n\n\n

=a2<\/sup>x2<\/sup>-{(by)2<\/sup>-2(by)(cz)+(cz)2<\/sup>}<\/p>\n\n\n\n

=a2<\/sup>x2<\/sup>-b2<\/sup>y2<\/sup>+2bcyz-c2<\/sup>z2<\/sup><\/p>\n\n\n\n

 (\u099e) (3a -10)(3a – 5)<\/strong><\/p>\n\n\n\n

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

(3a -10)(3a – 5)<\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/p>\n\n\n\n

(x-a)(x-b)=x2<\/sup>-(a+b)x+ab<\/p>\n\n\n\n

\u2234(3a -10)(3a – 5)<\/p>\n\n\n\n

=(3a)2<\/sup>-(10+5)3a+(10)(5)<\/p>\n\n\n\n

=9a2<\/sup>-(15)3a+50<\/p>\n\n\n\n

=9a2<\/sup>-45a+50<\/p>\n\n\n\n

(\u099f) (5a + 2b – 3c)(5a + 2b +3c)<\/strong><\/p>\n\n\n\n

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

(5a + 2b – 3c)(5a + 2b +3c)<\/p>\n\n\n\n

={(5a + 2b) – (3c)}{(5a + 2b) + (3c)}<\/p>\n\n\n\n

=(5a + 2b)2<\/sup> – (3c)2<\/sup><\/p>\n\n\n\n

= (5a)2<\/sup> + 2(5a)(2b) + (2b)2<\/sup> – (3c)2<\/sup><\/p>\n\n\n\n

=25a2<\/sup> + 20ab + 4b2<\/sup> – 9c2<\/sup><\/p>\n\n\n\n

(\u09a0) (ax + by + 5)(ax + by + 3)<\/strong><\/p>\n\n\n\n

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

(ax + by + 5)(ax + by + 3)<\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/p>\n\n\n\n

(x+a)(x+b)=x2<\/sup>+(a+b)x+ab<\/p>\n\n\n\n

\u2234(ax + by + 5)(ax + by + 3)<\/p>\n\n\n\n

=(ax + by)2<\/sup> + (5 + 3)(ax + by) + (5)(3)<\/p>\n\n\n\n

=(ax)2<\/sup> + 2(ax)(by) + (by)2<\/sup> + 8(ax + by) +15<\/p>\n\n\n\n

=a2<\/sup> x2<\/sup> + 2abxy + b2<\/sup> y 2<\/sup> + 8ax + 8by) +15<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09ea\u0983 a=4, b=6 \u098f\u09ac\u0982 c=3 \u09b9\u09b2\u09c7 4a2<\/sup>b2<\/sup>-16ab2<\/sup>c+16b2<\/sup>c2<\/sup> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7,<\/p>\n\n\n\n

a=4, b=6 \u098f\u09ac\u0982 c=3<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf=4a2<\/sup>b2<\/sup>-16ab2<\/sup>c+16b2<\/sup>c2<\/sup><\/p>\n\n\n\n

            = (2ab)2<\/sup> \u2013 2* 2ab * 4bc + (4bc)2<\/sup><\/p>\n\n\n\n

=(2ab – 4bc)2<\/sup><\/p>\n\n\n\n

= (2 * 4* 6 – 4 * 6* 3)2<\/sup>          [a, b \u0993 c \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

=(48 – 72)2<\/sup><\/p>\n\n\n\n

= (-24)2<\/sup><\/p>\n\n\n\n

=576<\/p>\n\n\n\n

\u09a8\u09bf\u09b0\u09cd\u09a8\u09c7\u09af\u09bc \u09ae\u09be\u09a8 576<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09eb\u0983 x-1\/x=3 \u09b9\u09b2\u09c7, x2<\/sup>+1\/x2 <\/sup>\u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x-1\/x=3<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= x2<\/sup>+1\/x2<\/sup><\/p>\n\n\n\n

            =(x-1\/x)2<\/sup>+2*x*1\/x<\/p>\n\n\n\n

            =32<\/sup>+2 (\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7)<\/p>\n\n\n\n

            =9+2<\/p>\n\n\n\n

            =11<\/p>\n\n\n\n

\u09a8\u09bf\u09b0\u09cd\u09a8\u09c7\u09af\u09bc \u09ae\u09be\u09a8 11<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09ec\u0983 a+1\/a=4 \u09b9\u09b2\u09c7, a4<\/sup>+1\/a4 <\/sup>\u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a+1\/a=4<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a4<\/sup>+1\/a4<\/sup><\/p>\n\n\n\n

            =(a2<\/sup>)2<\/sup>+(1\/a2<\/sup>)2<\/sup><\/p>\n\n\n\n

                <\/sup>=(a2<\/sup>+1\/a2<\/sup>)2<\/sup>-2*a2<\/sup>*1\/a2<\/sup><\/p>\n\n\n\n

            ={(a+1\/a)2<\/sup>-2*a*1\/a}-2<\/p>\n\n\n\n

            ={(4)2<\/sup>-2}2<\/sup>-2    [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

            =(16-2)2<\/sup>-2<\/p>\n\n\n\n

            =(14)2<\/sup>-2<\/p>\n\n\n\n

=196-2<\/p>\n\n\n\n

=194<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09ed\u0983  m = 6, n = 7 \u09b9\u09b2\u09c7, 16(m2<\/sup> + n 2<\/sup> )2<\/sup> + 56(m2<\/sup> + n 2<\/sup>)(3m2<\/sup> – 2n 2<\/sup>) + 49(3m2<\/sup> – 2n 2<\/sup>)2<\/sup> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, m2<\/sup>+n2<\/sup>=a<\/p>\n\n\n\n

\u098f\u09ac\u0982 3m2<\/sup>-2n2<\/sup>=b<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf=16(m2 <\/sup>+ n2<\/sup>)2<\/sup> + 56(m2<\/sup> + n2<\/sup>)(3m2<\/sup> – 2n2<\/sup>) + 49(3m2<\/sup> – 2n2<\/sup>)2<\/sup><\/p>\n\n\n\n

                  = 16(a) 2<\/sup> +56(a)(b) + 49(b) 2<\/sup><\/p>\n\n\n\n

= (4a)2<\/sup> + 2(4a)(7b) + (7b)2<\/sup><\/p>\n\n\n\n

= (4a + 7b)2<\/sup><\/p>\n\n\n\n

= {4(m2<\/sup> + n2<\/sup> ) + 7(3m2<\/sup> – 2n2<\/sup> )}2<\/sup>   [\u09ae\u09be\u09a8 \u09ac\u09bf\u09b8\u09c7\u09af\u09bc]<\/p>\n\n\n\n

= {4m2<\/sup> + 4n2<\/sup> + 21m2<\/sup> – 14 n2<\/sup>}2<\/sup><\/p>\n\n\n\n

= {25m2<\/sup> – 10 n2<\/sup>}2<\/sup><\/p>\n\n\n\n

= {25 * (6)2<\/sup> – 10 * (7)2<\/sup> )}2<\/sup>  [ m \u0993 n \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

= {25 * 36 – 10 * 49}2<\/sup><\/p>\n\n\n\n

= {900 – 490}2<\/sup><\/p>\n\n\n\n

= {410}2<\/sup><\/p>\n\n\n\n

= 168100<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09ee\u0983  a-1\/a=m\u09b9\u09b2\u09c7, \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, a4<\/sup>+1\/a4<\/sup>=m4<\/sup>+4m2<\/sup>+2<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a-1\/a=m<\/p>\n\n\n\n

\u09a6\u09c7\u0996\u09be\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, a4<\/sup>+1\/a4<\/sup>=m4<\/sup>+4m2<\/sup>+2<\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09cd\u09aa\u0995\u09cd\u09b7= a4<\/sup>+1\/a4<\/sup><\/p>\n\n\n\n

                <\/sup>=(a2<\/sup>)2<\/sup>+(1\/a2<\/sup>)2<\/sup><\/p>\n\n\n\n

            =(a2<\/sup>+1\/a2<\/sup>)2<\/sup>-2*a2<\/sup>*1\/a2<\/sup><\/p>\n\n\n\n

            ={(a-1\/a)2<\/sup>+2*a*1\/a}2<\/sup>-2<\/p>\n\n\n\n

            ={(m)2<\/sup>+2}2<\/sup>-2              [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

            =(m2<\/sup>)2<\/sup>+2*m2<\/sup>*2+22<\/sup>-2<\/p>\n\n\n\n

            =m4<\/sup>+4m2<\/sup>+4-2<\/p>\n\n\n\n

            =m4<\/sup>+4m2<\/sup>+2<\/p>\n\n\n\n

=\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb)<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09ef\u0983 x-1\/x=4 \u09b9\u09b2\u09c7, \u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0 \u09af\u09c7, x2<\/sup>+(1\/x)2<\/sup>=18<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7,  x-1\/x=4<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, x2<\/sup>+(1\/x)2<\/sup>=18<\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7= x2<\/sup>+(1\/x)2<\/sup><\/p>\n\n\n\n

                <\/sup>=(x-1\/x)2<\/sup>+2*x*1\/x<\/p>\n\n\n\n

            =(4)2<\/sup>+2          [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

            =16+2<\/p>\n\n\n\n

            =18<\/p>\n\n\n\n

=\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09aa\u09cd\u09b0\u09ae\u09be\u09a8\u09bf\u09a4)\u0964<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e7\u09e6\u0983 m+1\/m=2 \u09b9\u09b2\u09c7, \u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0 \u09af\u09c7, m4<\/sup>+1\/m4<\/sup>=2<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, m+1\/m=2<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, m4<\/sup>+1\/m4<\/sup>=2<\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7= m4<\/sup>+1\/m4<\/sup><\/p>\n\n\n\n

=(m2<\/sup>)2<\/sup>+(1\/m2<\/sup>)<\/p>\n\n\n\n

=(m2<\/sup>+1\/m2<\/sup>)2<\/sup>-2*m2<\/sup>*1\/m2<\/sup><\/p>\n\n\n\n

={(m+1\/m)2<\/sup>-2*m*1\/m}2<\/sup>-2<\/p>\n\n\n\n

={(2)2<\/sup>-2)}2<\/sup>-2   [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

=22<\/sup>-2<\/p>\n\n\n\n

=4-2<\/p>\n\n\n\n

=2<\/p>\n\n\n\n

=\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 [\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4] <\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e7\u09e7\u0983 x+y=12 \u098f\u09ac\u0982 xy=27 \u09b9\u09b2\u09c7, (x-y)2 <\/sup>\u0993 x2<\/sup>+y2 <\/sup>\u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x+y=12 \u098f\u09ac\u0982 xy=27<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a5\u09ae \u09b0\u09be\u09b6\u09bf=(x-y)2<\/sup><\/p>\n\n\n\n

                        =(x+y)2<\/sup>-4xy<\/p>\n\n\n\n

                        =(12)2<\/sup>-4*27<\/p>\n\n\n\n

                        =144-108<\/p>\n\n\n\n

                        =36<\/p>\n\n\n\n

\u098f\u09ac\u0982 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf= x2<\/sup>+y2          <\/sup><\/p>\n\n\n\n

                        =(x+y)2<\/sup>-2xy<\/p>\n\n\n\n

                        =(12)2<\/sup>-2*27<\/p>\n\n\n\n

                        =144-54<\/p>\n\n\n\n

                        =90<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e7\u09e8\u0983 a+b=13 \u098f\u09ac\u0982 a-b=3 \u09b9\u09b2\u09c7, 2a2<\/sup>+2b2<\/sup> \u0993 ab \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

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

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a+b=13 \u098f\u09ac\u0982 a-b=3<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a5\u09ae \u09b0\u09be\u09b6\u09bf=2a2<\/sup>+2b2<\/sup><\/p>\n\n\n\n

            =2(a2<\/sup>+b2<\/sup>)<\/p>\n\n\n\n

            =(a+b)2<\/sup>+(a-b)2<\/sup><\/p>\n\n\n\n

            =(13)2<\/sup>+32<\/sup><\/p>\n\n\n\n

                <\/sup>=169+9         <\/p>\n\n\n\n

            =178<\/p>\n\n\n\n

\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09b0\u09be\u09b6\u09bf= ab<\/p>\n\n\n\n

            ={(a+b)\/2}2<\/sup>-{(a-b)\/2}2<\/sup><\/p>\n\n\n\n

            =(13\/2)2<\/sup>-(3\/2)2<\/sup><\/p>\n\n\n\n

            =169\/4-9\/4<\/p>\n\n\n\n

            =160\/4<\/p>\n\n\n\n

            =40<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09e7\u09e9\u0983 \u09a6\u09c1\u0987\u099f\u09bf \u09b0\u09be\u09b6\u09bf\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0 \u09b0\u09c1\u09aa\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

(\u0995) (5 p – 3q)( p + 7q)          (\u0996) (6a + 9b)(7b – 8a)<\/p>\n\n\n\n

(\u0997) (3x +5 y)(7x – 5 y)           (\u0998) (5x +13)(5x -13)<\/p>\n\n\n\n

(\u0995) (5 p – 3q)( p + 7q)<\/strong><\/p>\n\n\n\n

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

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, ab={(a+b)\/2}2<\/sup>-{(a-b)\/2}2<\/sup><\/p>\n\n\n\n

\u2234(5 p – 3q)( p + 7q) =[{(5 p – 3q)+( p + 7q)}\/2]2<\/sup>– [{(5 p – 3q)-( p + 7q)}\/2]2<\/sup><\/p>\n\n\n\n

                                    =[{5 p – 3+ p + 7q}\/2]2<\/sup>– [{5 p – 3q-p – 7q}\/2]2<\/sup><\/p>\n\n\n\n

                                    =[{6p + 4q}\/2]2<\/sup>– [{4p – 10q}\/2]2<\/sup><\/p>\n\n\n\n

                                    =[2{3p + 2q}\/2]2<\/sup>– [2{2p – 5q}\/2]2<\/sup><\/p>\n\n\n\n

                                     <\/sup>={3p + 2q}2<\/sup>– {2p – 5q}2<\/sup><\/p>\n\n\n\n

(\u0996) (6a + 9b)(7b – 8a)<\/strong><\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, ab={(a+b)\/2}2<\/sup>-{(a-b)\/2}2<\/sup><\/p>\n\n\n\n

\u2234(6a + 9b)(7b – 8a)= =[{(6a +9b)+( 7b \u2013 8a)}\/2]2<\/sup>– [{(6a +9b)-( 7b -8a)}\/2]2<\/sup><\/p>\n\n\n\n

=[{6a +9b+7b \u2013 8a}\/2]2<\/sup>– [{6a +9b- 7b +8a}\/2]2<\/sup><\/p>\n\n\n\n

=[{16a  \u2013 2a}\/2]2<\/sup>– [{14a +2b}\/2]2<\/sup><\/p>\n\n\n\n

=[2{8a  \u2013 a}\/2]2<\/sup>– [2{7a +b}\/2]2<\/sup><\/p>\n\n\n\n

={8a  \u2013 a}2<\/sup>– {7a +b}2<\/sup><\/p>\n\n\n\n

(\u0997) (3x +5 y)(7x – 5 y)<\/strong><\/p>\n\n\n\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, ab={(a+b)\/2}2<\/sup>-{(a-b)\/2}2<\/sup><\/p>\n\n\n\n

\u2234(3x +5 y)(7x – 5 y) =[{(3x +5y)+( 7x \u2013 5y)}\/2]2<\/sup>– [{(3x +5y)-( 7x -5y)}\/2]2<\/sup><\/p>\n\n\n\n

                          =[{3x +5y+7x \u2013 5y}\/2]2<\/sup>– [{3x +5y- 7x +5y}\/2]2<\/sup><\/p>\n\n\n\n

=[{10x}\/2]2<\/sup>– [{-4x +10y}\/2]2<\/sup><\/p>\n\n\n\n

={5x}2<\/sup>– [-2{2x -5y}\/2]2<\/sup><\/p>\n\n\n\n

={5x}2<\/sup>– {2x -5y}2<\/sup><\/p>\n\n\n\n

(\u0998) (5x +13)(5x -13)<\/strong><\/p>\n\n\n\n

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

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, ab={(a+b)\/2}2<\/sup>-{(a-b)\/2}2<\/sup><\/p>\n\n\n\n

\u2234(5x +13)(5x -13) =[{(5x +13)+( 5x \u2013 13)}\/2]2<\/sup>– [{(5x +13)-( 5x -13)}\/2]2<\/sup><\/p>\n\n\n\n

=[{5x +13+5x \u2013 13}\/2]2<\/sup>– [{5x +13- 5x +13}\/2]2<\/sup><\/p>\n\n\n\n

=[{10x}\/2]2<\/sup>-(26\/2)2<\/sup><\/p>\n\n\n\n

=(5x)2<\/sup>-(13)2<\/sup><\/p>\n\n\n\n

\n\n\n\n
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tags: <\/em>Bangladesh, Bangla, Bengali, Class 8\/JSC math BD, Class eight math solution bd, class 8 math pdf download, \u0985\u09b7\u09cd\u099f\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf\u09b0 \u0997\u09a3\u09bf\u09a4 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ea.\u09e7 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09df \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u0964\r<\/pre>\n","protected":false},"excerpt":{"rendered":"
\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u09ee\u09ae \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 Eight (08) Math Book Solution | Chapter 04 : Algebraic formulas and applications| Class 8 math book Online Solution in Bangla (BD) \u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997| \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e7: \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 – PDF \u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf […]<\/p>\n","protected":false},"author":1,"featured_media":4919,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","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":[36],"tags":[37,38],"class_list":["post-4959","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-eight-8","tag-class-8","tag-class-eight"],"yoast_head":"\n\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e7 | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD<\/title>\n<meta name=\"description\" content=\"\u09ee\u09ae \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 Eight (08) Math Book Solution. 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