Class:9-10( অনুশীলনী:৩.১,৩.২,৩.৩,৩.৪- এর বহুনির্বাচনী(3)।

Class:9-10_math_img

1) \displaystyle ( x+3)( x-3) =16 হলে \displaystyle x এর মান কত?
\displaystyle \Longrightarrow x^{2} -3^{2}=16 আমরা জানি,,\displaystyle (a+b)\displaystyle ( a-b) =a^{2} -b^{2}
\displaystyle \Longrightarrow x^{2} -9=16
\displaystyle \Longrightarrow x^{2} =16+9
\displaystyle \Longrightarrow x^{2} =25
\displaystyle \Longrightarrow x=\pm 5

Class:9-10_math_img

2) \displaystyle a=\sqrt{2}, \displaystyle b=\sqrt{3} ,\displaystyle ( a+b)^{2} -2ab এর মান নির্নয় কর।
দেওয়া আছে,,,
\displaystyle a=\sqrt{2} এবং \displaystyle b=\sqrt{3}
\displaystyle প্রদওরাশি=( a+b)^{2} -2ab
\displaystyle =a^{2} +2ab+b^{2} -2ab
\displaystyle =a^{2} +b^{2}
\displaystyle =\left(\sqrt{2}\right)^{2}+\displaystyle \left(\sqrt{3}\right)^{2}
\displaystyle =2+3
\displaystyle =5

Class:9-10_math_img

3) \displaystyle \left( x^{2} +1\right)^{2} =5x^{2} হলে, \displaystyle x+\frac{1}{x} এর মান কত ?

class:9-10_math_img .

4) \displaystyle p+q=5 এবং \displaystyle p-q=3 হলে , \displaystyle p^{2} +q^{2}এর মান নির্নয় কর?
দেওয়া আছে,,
\displaystyle p+q=5 এবং \displaystyle p-q=3
আমরা জানি,,
\displaystyle 2\left( p^{2} +q^{2}\right) =( p+q)^{2} +( p-q)^{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{( p+q)^{2} +( p-q)^{2}}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{( 5)^{2} +( 3)^{2}}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{25+9}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{34}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =17

Class:9-10_math_img.

5) \displaystyle ( -2x-3y) \এর বর্গ নির্নয় কর।
\displaystyle ={-( 2x+3y)}^{2}
\displaystyle =( 2x+3y)^{2}
\displaystyle =( 2x)^{2} +2.3y.2x+( 3y)^{2}
\displaystyle =2^{2} .x^{2} +12xy+3^{2} .y^{2}
\displaystyle =4x^{2} +12xy+9y^{2}

Class:9-10_math_img.

6) \displaystyle 4x^{2} +2 এর সাথে কত (+) করলে যোগফল পূর্নবর্গ হবে?
\displaystyle =4x^{2} +2+\frac{1}{4x^{2}}
\displaystyle =( 2x)^{2} +2.2x.\frac{1}{2x} +\left(\frac{1}{2x}\right)^{2}
\displaystyle =\left( 2x+\frac{1}{2x}\right)^{2}
সুতরাং \displaystyle 4x^{2} +2 এর সাথে \displaystyle \frac{1}{4x^{2}} (+) করলে যোগফল পূর্নবর্গ হবে ।

Class:9-10_math_img

7) \displaystyle \frac{1}{2}\left{( 2x+3y)^{2} +( 2x-3y)^{2}\right}= কত?

\displaystyle =\frac{1}{2} .2\left{( 2x)^{2} +( 3y)^{2}\right}
\displaystyle =2^{2} .x^{2} +3^{2} .y^{2}
\displaystyle =4x^{2} +9y^{2}

Class:9-10_math_img

8) \displaystyle h+\frac{1}{h} =6 হলে, \displaystyle \left( h-\frac{1}{h}\right) এর মান নির্নয় কর।
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right)^{2} =\left( h+\frac{1}{h}\right)^{2} -4.h.\frac{1}{h}
\displaystyle \Longrightarrow \sqrt{\left( h-\frac{1}{h}\right)^{2}}=\displaystyle \sqrt{\left( h+\frac{1}{h}\right)^{2} -4.h.\frac{1}{h}}
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right) =\sqrt{\left( h+\frac{1}{h}\right)^{2} -4.h.\frac{1}{h}}
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right) =\sqrt{( 6)^{2} -4}
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right) =\sqrt{36-4}
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right) =\pm \sqrt{32}
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right) =\pm \sqrt{16.2}
\displaystyle \Longrightarrow \left( h-\frac{1}{h}\right) =\pm 4\sqrt{2}


class:9-10_math_img.
9) \displaystyle x-y=2 , \displaystyle xy=24  হলে \displaystyle ( x+y) এর মান কত?

দেওয়া আছে,,,
\displaystyle x-y=2 এবং \displaystyle xy=24

class:9-10_math_img.

10) \displaystyle y^{2} +\frac{1}{y^{2}} =6 হলে \displaystyle \left( y+\frac{1}{y}\right) এর মান কত?

Class:9-10_math_img.

11) \displaystyle b+\frac{2}{b} =3 হলে,, \displaystyle \left( b-\frac{2}{b}\right)^{2}এর মান কত?
দেওয়া আছ,,
\displaystyle b+\frac{2}{b} =3
এখন,,
\displaystyle \left( b-\frac{2}{b}\right)^{2} =\left( b+\frac{2}{b}\right)^{2} -4.b.\frac{2}{b}
\displaystyle =( 3)^{2} -4.2
\displaystyle =9-8
\displaystyle =1

Class:9-10_math_img.

12) যদি \displaystyle p+q=\sqrt{5} এবং \displaystyle p-q=\sqrt{3} হয়, তবে \displaystyle p^{2} +q^{2} এর মান কত?
দেওয়া আছে,,
\displaystyle p+q=\sqrt{5}
এবং, \displaystyle p-q=\sqrt{3}
এখন,
\displaystyle 2\left( p^{2} +q^{2}\right) =( p+q)^{2} +( p-q)^{2}
\displaystyle \left( p^{2} +q^{2}\right) =\frac{( p+q)^{2} +( p-q)^{2}}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{\left(\sqrt{5}\right)^{2} +\left(\sqrt{3}\right)^{2}}{2}

\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{5+3}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =\frac{8}{2}
\displaystyle \Longrightarrow \left( p^{2} +q^{2}\right) =4

Class:9-10_math_img

13) \displaystyle x+\frac{1}{x} =3 হলে,, \displaystyle x^{2} +\frac{1}{x^{2}} এর মান কত?
দেওয়া আছে,,
\displaystyle x+\frac{1}{x} =3
এখন,,
\displaystyle x^{2} +\frac{1}{x^{2}} =\left( x+\frac{1}{x}\right)^{2} -2.x.\frac{1}{x}
\displaystyle =( 3)^{2} -2
\displaystyle =9-2
\displaystyle =7

Class:9-10_math_img

14) \displaystyle a+\frac{1}{a} =\sqrt{2} হলে, \displaystyle a^{2} +\frac{1}{a^{2}} এর মান কত?
দেওয়া আছে,,
\displaystyle a+\frac{1}{a} =\sqrt{2}
এখন,,
\displaystyle a^{2} +\frac{1}{a^{2}} =\left( a+\frac{1}{a}\right)^{2} -2.a.\frac{1}{a}
\displaystyle =\left(\sqrt{2}\right)^{2} -2
\displaystyle =2-2
\displaystyle =0

Class:9-10_math_img

15) \displaystyle a^{2} +\frac{1}{a^{2}} =2 হলে, \displaystyle a+\frac{1}{a}এর মান কত ?
দেওয়া আছে,,,
\displaystyle a^{2} +\frac{1}{a^{2}} =2
এখন,,
\displaystyle \left( a+\frac{1}{a}\right)^{2} =a^{2} +2.a.\frac{1}{a} +\frac{1}{a^{2}}
\displaystyle \Longrightarrow \left( a+\frac{1}{a}\right)^{2} =a^{2} +\frac{1}{a^{2}} +2
\displaystyle \Longrightarrow \left( a+\frac{1}{a}\right)^{2} =2+2
\displaystyle \Longrightarrow \left( a+\frac{1}{a}\right)^{2} =4
\displaystyle \Longrightarrow \sqrt{\left( a+\frac{1}{a}\right)^{2}}\displaystyle =\pm \sqrt{4}

Class:9-10_math_img

16) \displaystyle p-\frac{1}{p} =3 হলে, \displaystyle p^{2} +\frac{1}{p^{2}} এর মান কত ?
দেওয়া আছে,,
\displaystyle p-\frac{1}{p} =3
এখন,,
\displaystyle p^{2} +\frac{1}{p^{2}} =\left( p-\frac{1}{p}\right)^{2} +2.p.\frac{1}{p}
\displaystyle =( 3)^{2} +2
\displaystyle =9+2
\displaystyle =11

class:9-10_math)_img

17) \displaystyle x=2+\sqrt{3} হলে,, \displaystyle x^{2} এর মান কত ?
\displaystyle =\left( 2+\sqrt{3}\right)^{2}
\displaystyle =( 2)^{2} +2.2.\sqrt{3}+\displaystyle \left(\sqrt{3}\right)^{2}
\displaystyle =4+4\sqrt{3}+\displaystyle 3
\displaystyle =7+4\sqrt{3}

Class:9-10_math_img

18) \displaystyle ( a+b-c)^{2} =কত?
ধরি,,
\displaystyle a+b=m
\displaystyle =( m-c)^{2}
\displaystyle =m^{2} -2.m.c+c^{2}
\displaystyle =( a+b)^{2} -2( a+b) .c+c^{2}
\displaystyle =a^{2} +2ab+b^{2} -2ac-2bc+c^{2}
\displaystyle =a^{2} +b^{2} +c^{2} +2ab-2bc-2ac

Class:9-10_math_img.

19) \displaystyle a+b=3 এবং \displaystyle ab=2 হলে,, \displaystyle a^{2} -ab+b^{2}এর মান নির্নয় কর।
দেওয়া আছে,,
\displaystyle a+b=3
এবং,
\displaystyle ab=2
এখন,
\displaystyle a^{2} -ab+b^{2}
\displaystyle =\left( a^{2} +b^{2} -ab\right)
\displaystyle =( a+b)^{2} -2ab-ab
\displaystyle =( 3)^{2} -2.2-2
\displaystyle =9-4-2
\displaystyle =9-6
\displaystyle =3

Class:9-10_math_img.

20) \displaystyle m+n=8 এবং \displaystyle mn=15 , \displaystyle ( m-n)^{2}এর মান কত ?
দেওয়া আছে,,
\displaystyle m+n=8
এবং \displaystyle mn=15
এখন,
\displaystyle ( m-n)^{2} =( m+n)^{2} -4ab
\displaystyle =( 8)^{2} -4.15
\displaystyle =64-60
\displaystyle =4

Class:9-10_math_img.

21) \displaystyle a+b=1 এবং \displaystyle ab=4 হলে,\displaystyle ( a-b)^{2} এর মান কত?
দেওয়া আছে,,
\displaystyle a+b=1
এবং, \displaystyle ab=4
এখন,
\displaystyle ( a-b)^{2} =( a+b)^{2} -4ab
\displaystyle =( 1)^{2} -4.4
\displaystyle =1-16
\displaystyle =-15

Post Author: showrob

2 thoughts on “Class:9-10( অনুশীলনী:৩.১,৩.২,৩.৩,৩.৪- এর বহুনির্বাচনী(3)।

    soikot

    (March 29, 2020 - 1:29 pm)

    very goods math.

      showrob

      (March 31, 2020 - 2:28 pm)

      Thanks

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