{"id":4517,"date":"2022-09-24T20:35:30","date_gmt":"2022-09-24T20:35:30","guid":{"rendered":"https:\/\/www.studyzonebd.com\/math\/?p=4517"},"modified":"2022-09-24T23:58:44","modified_gmt":"2022-09-24T23:58:44","slug":"class-7-chapter-5-lesson-5-1","status":"publish","type":"post","link":"https:\/\/www.studyzonebd.com\/math\/class-7-chapter-5-lesson-5-1\/","title":{"rendered":"\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7 | \u09b8\u09aa\u09cd\u09a4\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf"},"content":{"rendered":"\n

\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u09ed\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 Seven (07) Math <\/a>Book Solution | Chapter <\/a>05 : Algebraic formulas and applications<\/p>\n\n\n\n

\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7:  \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09ac\u09b0\u09cd\u0997 \u0993 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc<\/h4>\n\n\n\n

\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\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 \u09ed\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

\u09ed\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf\u09b0 \u0997\u09a3\u09bf\u09a4 \u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/span><\/h4>\n\n\n\n

\u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09ac\u09b0\u09cd\u0997 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0 (\u09e7-\u09e7\u09ec<\/strong>):<\/strong><\/p>\n\n\n\n

\u09e7<\/strong>. a+5<\/strong><\/p>\n\n\n\n

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

(a+5) \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(a+5)2
<\/sup>=(a)2<\/sup>+2\u2715a\u27155+(5)2
<\/sup>=a2<\/sup>+10a+25<\/a><\/p>\n\n\n\n

\u09e8<\/strong>. 5x-7<\/strong><\/p>\n\n\n\n

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

5x-7 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
(5x-7)2
<\/sup>=(5x)2<\/sup>-2\u27155x\u27157+(7)2
<\/sup>=25x2<\/sup>-70x+49<\/p>\n\n\n\n

\u09e9<\/strong>. 3a-11xy<\/strong><\/p>\n\n\n\n

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

3a-11xy \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(3a)2<\/sup>-2\u27153a\u271511xy+(11xy)2
<\/sup>=9a2<\/sup>-66axy+121x2<\/sup>y2<\/sup><\/p>\n\n\n\n

\u09ea<\/strong>. 5a2<\/sup>+9m2<\/sup><\/strong><\/p>\n\n\n\n

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

(5a2<\/sup>+9m2<\/sup>) \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(5a2<\/sup>+9m2<\/sup>)2
<\/sup>=(5a2<\/sup>)2<\/sup>+2\u27155a2<\/sup>\u27159m2<\/sup>+(9m2<\/sup>)2
<\/sup>=25a4<\/sup>+90a2<\/sup>m2<\/sup>+81m4<\/sup><\/p>\n\n\n\n

\u09eb<\/strong>. 55<\/strong><\/p>\n\n\n\n

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

55 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(55)2
<\/sup>=(50+5)2
<\/sup>=(50)2<\/sup>+2\u271550\u27155+(5)2
<\/sup>=2500+500+25
=3025<\/p>\n\n\n\n

\u09ec<\/strong>. 990<\/strong><\/p>\n\n\n\n

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

990 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
(1000-10)2
<\/sup>=(1000)2<\/sup>-2\u27151000\u271510+(10)2
<\/sup>=1000000-20000+100
=980100<\/p>\n\n\n\n

\u09ed<\/strong>. xy-6y<\/strong><\/p>\n\n\n\n

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

xy-6y \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(xy-6y)2
<\/sup>=(xy)2<\/sup>-2\u2715xy\u27156y+(6y)2
<\/sup>=x2<\/sup>y2<\/sup>-12xy2<\/sup>+36y2<\/sup><\/p>\n\n\n\n

\u09ee<\/strong>. ax-by<\/strong><\/p>\n\n\n\n

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

ax-by \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
(ax-by)2
<\/sup>=(ax)2<\/sup>-2\u2715ax\u2715by+(by)2
<\/sup>=a2<\/sup>x2<\/sup>-2axby+b2<\/sup>y2<\/sup><\/p>\n\n\n\n

\u09ef<\/strong>. 97<\/strong><\/p>\n\n\n\n

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

97 \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(97)2
<\/sup>=(100-3)2
<\/sup>=(100)2<\/sup>-2\u2715100\u27153+(3)2
<\/sup>=10000-600+9
=9409<\/p>\n\n\n\n

\u09e7\u09e6<\/strong>. 2x+y-z<\/strong><\/p>\n\n\n\n

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

2x+y-z \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(2x+y-z)2
<\/sup>={(2x+y)-z}2
<\/sup>={(2x+y)2<\/sup>-2\u2715(2x+y)\u2715z+(z)2<\/sup>}
={(2x)2<\/sup>+2\u27152x\u2715y+(y)2<\/sup>-2\u27152x\u2715z-2\u2715y\u2715z+(z)2<\/sup>}
=4x2<\/sup>+4xy+y2<\/sup>-4xz-2yz+z2<\/sup><\/p>\n\n\n\n

\u09e7\u09e7<\/strong>. 2a-b+3c<\/strong><\/p>\n\n\n\n

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

2a-b+3c  \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(2a-b+3c)2
<\/sup>={(2a-b)2<\/sup>-2\u2715(2a-b)\u27153c+(3c)2<\/sup>}
={(2a)2<\/sup>-2\u27152a\u2715b+(b)2<\/sup>-2\u2715(2a-b)\u27153c+(3c)2<\/sup>}
=4a2<\/sup><\/p>\n\n\n\n

\u09e7\u09e8<\/strong>. x2<\/sup>+y2<\/sup>-z2<\/sup><\/strong><\/p>\n\n\n\n

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

x2<\/sup>+y2<\/sup>-z2 <\/sup>\u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(x2<\/sup>+y2<\/sup>-z2<\/sup>)2
<\/sup>={(x2<\/sup>+y2<\/sup>)2<\/sup>-2\u2715(x2<\/sup>+y2<\/sup>)\u2715z2<\/sup>+(z2<\/sup>)2<\/sup>}
={(x2<\/sup>)2<\/sup>+2\u2715x2<\/sup>\u2715y2<\/sup>+(y2<\/sup>)2<\/sup>-2\u2715(x2<\/sup>+y2<\/sup>)\u2715z2<\/sup>+(z2<\/sup>)2<\/sup>}
=x4<\/sup>+2x2<\/sup>y2<\/sup>+y4<\/sup>-2x2<\/sup>z2<\/sup>-2y2<\/sup>z2<\/sup>+z4<\/sup><\/p>\n\n\n\n

\u09e7\u09e9<\/strong>. a-2b-c<\/strong><\/p>\n\n\n\n

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

a-2b-c \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(a-2b-c)2
<\/sup>={(a-2b)-c}2
<\/sup>={(a-2b)2<\/sup>-2\u2715(a-2b)\u2715c+c2<\/sup>}
={a2<\/sup>-2\u2715a\u27152b+(2b)2<\/sup>-2ac+4bc+c2<\/sup>}
=a2<\/sup>-4ab+4b2<\/sup>-2ac+4bc+c2<\/sup><\/p>\n\n\n\n

\u09e7\u09ea<\/strong>. 3x-2y+z<\/strong><\/p>\n\n\n\n

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

3x-2y+z  \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
(3x-2y+z)2
<\/sup>={(3x-2y)2<\/sup>+2\u2715(3x-2y)\u2715z+z2<\/sup>}
={(3x)2<\/sup>-2\u27153x\u27152y+(2y)2<\/sup>+6xz-4yz+z2<\/sup>}
=9x2<\/sup>-12xy+4y2<\/sup>+6xz-4yz+z2<\/sup><\/p>\n\n\n\n

\u09e7\u09eb<\/strong>. bc+ca+ab<\/strong><\/p>\n\n\n\n

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

bc+ca+ab \u098f\u09b0 \u09ac\u09b0\u09cd\u0997
=(bc+ca+ab)2
<\/sup>={(bc+ca)2<\/sup>+2\u2715(bc+ca)\u2715ab+(ab)2<\/sup>}
={(bc)2<\/sup>+2\u2715bc\u2715ca+(ca)2<\/sup>+2\u2715bc\u2715ab-2\u2715ca\u2715ab+a2<\/sup>b2<\/sup>}
=b2<\/sup>c2<\/sup>+2abc2<\/sup>+a2<\/sup>c2<\/sup>+2ab2<\/sup>c+2a2<\/sup>bc+a2<\/sup>b2<\/sup><\/p>\n\n\n\n

\u09e7\u09ec<\/strong>. 2a2<\/sup>+2b-c2<\/sup><\/strong><\/p>\n\n\n\n

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

2a2<\/sup>+2b-c2 <\/sup>\u098f\u09b0 \u09ac\u09b0\u09cd\u0997
(2a2<\/sup>+2b-c2<\/sup>)2
<\/sup>={(2a2<\/sup>+2b)-c2<\/sup>}2
<\/sup>=(2a2<\/sup>+2b)2<\/sup>-2\u2715(2a2<\/sup>+2b)\u2715c2<\/sup>+(c2<\/sup>)2
<\/sup>=(2a2<\/sup>)2<\/sup>+2\u27152a2<\/sup>\u27152b+(2b)2<\/sup>-2\u27152a2<\/sup>\u2715c2<\/sup>-2\u27152b\u2715c2<\/sup>+c4
<\/sup>=4a4<\/sup>+8a2<\/sup>b+4b2<\/sup>-4a2<\/sup>c2<\/sup>-4bc2<\/sup>+c4<\/sup><\/p>\n\n\n\n

\u09b8\u09b0\u09b2<\/strong> <\/strong>\u0995\u09b0<\/strong> (<\/strong>\u09e7\u09ed<\/strong>–<\/strong>\u09e8\u09ea<\/strong>):<\/strong><\/p>\n\n\n\n

\u09e7\u09ed<\/strong>. (2a+1)2<\/sup>-4a(2a+1)+4a2<\/sup><\/strong><\/p>\n\n\n\n

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

(2a+1)2<\/sup>-4a(2a+1)+4a2
<\/sup>=(2a+1)2<\/sup>-2\u27152a\u2715(2a+1)+(2a)2
<\/sup>=(2a+1-2a)2
<\/sup>=(1)2
<\/sup>=1<\/p>\n\n\n\n

\u09e7\u09ee<\/strong>. (5a+3b)2<\/sup>+2(5a+3b)(4a-3b)+(4a-3b)2<\/sup><\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 5a+3b=x \u098f\u09ac\u0982 4a-3b=y
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=x2<\/sup>+2xy+y2
<\/sup>=(x+y)2
<\/sup>=(5a+3b+4a-3b)2 <\/sup> [x \u0993 y\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(9a)2
<\/sup>=81a2<\/sup><\/p>\n\n\n\n

\u09e7\u09ef<\/strong>. (7a+b)2<\/sup>-2(7a+b)(7a-b)+(7a-b)2<\/sup><\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 7a+b=x \u098f\u09ac\u0982 7a-b=y
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=x2<\/sup>-2xy+y2
<\/sup>=(x-y)2
<\/sup>=(7a+b-7a+b)2  <\/sup>[x \u0993 y\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(2b)2
<\/sup>=4b2<\/sup><\/p>\n\n\n\n

\u09e8\u09e6<\/strong>. (2x+3y)2<\/sup>+2(2x+3y)(2x-3y)+(2x-3y)2<\/sup><\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 2x+3y=a \u098f\u09ac\u0982 2x-3y=b
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=a2<\/sup>+2ab+b2
<\/sup>=(a+b)2
<\/sup>=(2x+3y+2x-3y)2<\/sup>  [ a \u0993 b \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(4x)2
<\/sup>=16x2<\/sup><\/p>\n\n\n\n

\u09e8\u09e7<\/strong>. (5x-2)2<\/sup>+(5x+7)2<\/sup>-2(5x-2)(5x+7)<\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 5x-2=a \u098f\u09ac\u0982 5x+7=b
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=a2<\/sup>+b2<\/sup>-2ab
=(a-b)2
<\/sup>=(5x-2-5x-7)2<\/sup>  [ a \u0993 b \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(-9)2
<\/sup>=81<\/p>\n\n\n\n

\u09e8\u09e8<\/strong>. (3ab-cd)2<\/sup>+9(cd-ab)2<\/sup>+6(3ab-cd)(cd-ab)<\/strong><\/p>\n\n\n\n

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

(3ab-cd)2<\/sup>+9(cd-ab)2<\/sup>+6(3ab-cd)(cd-ab)
=(3ab-cd)2<\/sup>+{3(cd-ab)}2<\/sup>+2\u27153(3ab-cd)(cd-ab)
\u09a7\u09b0\u09bf, 3ab-cd=x \u098f\u09ac\u0982 3(cd-ab)=y
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=x2<\/sup>+y2<\/sup>+2xy
=(x+y)2
<\/sup>=[(3ab-cd)+{3(cd-ab)}]2<\/sup>  [ x \u0993 y \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(3ab-cd+3cd-3ab)2
<\/sup>=(2cd)2
<\/sup>=4c2<\/sup>d2<\/sup><\/p>\n\n\n\n

\u09e8\u09e9<\/strong>. (2x+5y+3z)2<\/sup>+(5y+3z-x)2<\/sup>-2(5y+3z-x)(2x+5y+2z)<\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 2x+5y+3z=a \u098f\u09ac\u0982 5y+3z-x=b
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=a2<\/sup>-2ab+b2
<\/sup>=(a-b)2
<\/sup>=(2x+5y+3z-5y-3z+x)2 <\/sup>[ a \u0993 b \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(3x)2
<\/sup>=9x2<\/sup><\/p>\n\n\n\n

\u09e8\u09ea<\/strong>. (2a-3b+4c)2<\/sup>+(2a+3b-4c)2<\/sup>+2(2a-3b+4c)(2a+3b-4c)<\/strong><\/p>\n\n\n\n

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

\u09a7\u09b0\u09bf, 2a-3b+4c=x \u098f\u09ac\u0982 2a+3b-4c=y
\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=x2<\/sup>+y2<\/sup>+2xy
=(x+y)2
<\/sup>=(2a-3b+4c+2a+3b-4c)2<\/sup>  [ x \u0993 y \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(4a)2
<\/sup>=16a2<\/sup><\/p>\n\n\n\n

\u09ae\u09be\u09a8<\/strong> <\/strong>\u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc<\/strong> <\/strong>\u0995\u09b0<\/strong> (<\/strong>\u09e8\u09eb<\/strong>–<\/strong>\u09e8\u09ee<\/strong>):<\/strong><\/p>\n\n\n\n

\u09e8\u09eb<\/strong>. 25x2<\/sup>+36y2<\/sup>-60xy, <\/strong>\u09af\u0996\u09a8<\/strong> x=-4, y=-5<\/strong><\/p>\n\n\n\n

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

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=25x2<\/sup>+36y2<\/sup>-60xy
=(5x)2<\/sup>+(6y)2<\/sup>-2\u27155x\u27156y
=(5x-6y)2
<\/sup>={(5\u2715(-4)-6\u2715(-5)}2 <\/sup>[\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(-20+30)2
<\/sup>=(10)2
<\/sup>=100<\/p>\n\n\n\n

\u09e8\u09ec<\/strong>. 16a2<\/sup>-24ab+9b2<\/sup>, <\/strong>\u09af\u0996\u09a8<\/strong> a=7, b=6<\/strong><\/p>\n\n\n\n

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

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=16a2<\/sup>-24ab+9b2
<\/sup>=(4a)2<\/sup>-2\u27154a\u27153b+(3b)2
<\/sup>=(4a-3b)2
<\/sup>=(4\u27157-3\u27156)2 <\/sup>[\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(28-18)2
<\/sup>=(10)2
<\/sup>=100<\/p>\n\n\n\n

\u09e8\u09ed<\/strong>. 9x2<\/sup>+30x+25, <\/strong>\u09af\u0996\u09a8<\/strong> x=-2<\/strong><\/p>\n\n\n\n

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

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=9x2<\/sup>+30x+25
=(3x)2<\/sup>+2\u27153x\u27155+52
<\/sup>=(3x+5)2
<\/sup>={3\u2715(-2)+5}2<\/sup> [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(-6+5)2
<\/sup>=(-1)2
<\/sup>=1<\/p>\n\n\n\n

\u09e8\u09ee<\/strong>. 81a2<\/sup>+18ac+c2<\/sup>, <\/strong>\u09af\u0996\u09a8<\/strong> a=7, c=-67<\/strong><\/p>\n\n\n\n

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

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
=81a2<\/sup>+18ac+c2
<\/sup>=(9a)2<\/sup>+2\u27159a\u2715c+c2
<\/sup>=(9a+c)2
<\/sup>=(9\u27157-67)2 <\/sup>[\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(63-67)2
<\/sup>=(-4)2
<\/sup>=16<\/p>\n\n\n\n

\u09e8\u09ef<\/strong>. a-b=7 <\/strong>\u098f\u09ac\u0982<\/strong> ab=3 <\/strong>\u09b9\u09b2\u09c7<\/strong>, <\/strong>\u09a6\u09c7\u0996\u09be\u0993<\/strong> <\/strong>\u09af\u09c7<\/strong>, (a+b)2<\/sup>=61<\/strong><\/p>\n\n\n\n

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

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7
=(a+b)2
<\/sup>=(a-b)2<\/sup>+4ab
=72<\/sup>+4\u27153 [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=49+12
=61
=\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb)<\/p>\n\n\n\n

\u09e9\u09e6<\/strong>. a+b=5 <\/strong>\u098f\u09ac\u0982<\/strong> ab=12 <\/strong>\u09b9\u09b2\u09c7<\/strong>, <\/strong>\u09a6\u09c7\u0996\u09be\u0993<\/strong> <\/strong>\u09af\u09c7<\/strong>, a2<\/sup>+b2<\/sup>=1<\/strong><\/p>\n\n\n\n

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

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7
= a2<\/sup>+b2
<\/sup>=(a+b)2<\/sup>-2ab
=52<\/sup>-2\u271512 [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=25-24
=1
=\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb)<\/p>\n\n\n\n

\u09e9\u09e7<\/strong>. x+1\/x=5 <\/strong>\u09b9\u09b2\u09c7<\/strong>, <\/strong>\u09aa\u09cd\u09b0\u09ae\u09be\u09a8<\/strong> <\/strong>\u0995\u09b0<\/strong> <\/strong>\u09af\u09c7<\/strong>, (x2<\/sup>-1\/x2<\/sup>)2<\/sup>=525<\/strong><\/p>\n\n\n\n

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

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7
=(x2<\/sup>-1\/x2<\/sup>)2
<\/sup>=(x2<\/sup>+1\/x2<\/sup>)2<\/sup>-4\u2715x2<\/sup>\u27151\/x2
<\/sup>=(x2<\/sup>+1\/x2<\/sup>)2<\/sup>-4
={(x+1\/x)2<\/sup>-2\u2715x\u27151\/x}2<\/sup>-4
={(5)2<\/sup>-2}2<\/sup>-4
=(25-2)2<\/sup>-4
=(23)2<\/sup>-4
=529-4
=525
=\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e9\u09e8<\/strong>. a+b=8 <\/strong>\u098f\u09ac\u0982<\/strong> a-b=4 <\/strong>\u09b9\u09b2\u09c7<\/strong>, ab= <\/strong>\u0995\u09a4<\/strong>?<\/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>=(8\/2)2<\/sup>-(4\/2)2 <\/sup>[\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=(4)2<\/sup>-(2)2
<\/sup>=16-4
=12<\/p>\n\n\n\n

\u09e9\u09e9<\/strong>. x+y=7 <\/strong>\u098f\u09ac\u0982<\/strong> xy=10 <\/strong>\u09b9\u09b2\u09c7<\/strong>, x2<\/sup>+y2<\/sup>+5xy <\/strong>\u098f\u09b0<\/strong> <\/strong>\u09ae\u09be\u09a8<\/strong> <\/strong>\u0995\u09a4<\/strong>?<\/strong><\/p>\n\n\n\n

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

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf
= x2<\/sup>+y2<\/sup>+5xy
=(x+y)2<\/sup>-2xy+5xy
=(x+y)2<\/sup>+3xy
=(7)2<\/sup>+3\u271510 [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]
=49+30
=79<\/p>\n\n\n\n

\u09e9\u09ea. m+1\/m=2 \u09b9\u09b2\u09c7, \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7<\/strong>, 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
\u09ac\u09be, (m+1\/m)2<\/sup>=22 <\/sup>[\u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09ac\u09b0\u09cd\u0997 \u0995\u09b0\u09c7]
\u09ac\u09be, m2<\/sup>+2\u2715m\u27151\/m+(1\/m)2<\/sup>=4
\u09ac\u09be, m2<\/sup>+2+1\/m2<\/sup>=4
\u09ac\u09be, m2<\/sup>+1\/m2<\/sup>=4-2
\u09ac\u09be, (m2<\/sup>+1\/m2<\/sup>)2<\/sup>=(2)2
<\/sup>\u09ac\u09be, (m2<\/sup>)2<\/sup>+2\u2715m2<\/sup>\u27151\/m2<\/sup>+(1\/m2<\/sup>)2<\/sup>=4 [\u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09ac\u09b0\u09cd\u0997 \u0995\u09b0\u09c7]
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<\/sup>\u09ac\u09be, m4<\/sup>+1\/m4<\/sup>=4-2
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\n\n\n\n
tags: <\/em>Class 7 Math book solution BD pdf,Math lecture guide for class 7,class 7 math bd pdf,\u0997\u09a3\u09bf\u09a4 \u09b8\u09aa\u09cd\u09a4\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0-\u09eb.\u09e7 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09ac\u09b0\u09cd\u0997 \u0993 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u09ed\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 Seven (07) Math Book Solution | Chapter 05 : Algebraic formulas and applications \u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7:  \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09ac\u09b0\u09cd\u0997 \u0993 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7 \u098f\u09b0 \u09b8\u0995\u09b2 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 […]<\/p>\n","protected":false},"author":1,"featured_media":4333,"comment_status":"closed","ping_status":"closed","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":[33],"tags":[35,34],"class_list":["post-4517","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-seven-7","tag-class-7","tag-class-seven"],"yoast_head":"\n\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7 | \u09b8\u09aa\u09cd\u09a4\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD<\/title>\n<meta name=\"description\" content=\"\u09ed\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 Seven (07) Math Book Solution. Chapter 05 : Algebraic formulas and applications \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-7-chapter-5-lesson-5-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u09eb\u09ae \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \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 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09eb.\u09e7 | \u09b8\u09aa\u09cd\u09a4\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD\" \/>\n<meta property=\"og:description\" content=\"\u09ed\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 Seven (07) Math Book Solution. 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