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676 . $x^{2} - 3 x + 1 = 0$ হলে, এর $x + \frac{1}{x}$ এর মান নির্ণয় করুন।

A. 3
B. 2
C. 5
D. 8

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Answer: Option A

Explanation:

দেওয়া আছে, x^{2} -3x+1=0 \Rightarrow x^{2} + 1 = 3 x \Rightarrow \frac{x^{2} + 1}{x} = 3 \Rightarrow \frac{x^{2}}{x} + \frac{1}{x} = 3 ∴ x + \frac{1}{x} = 3

677 . $x + \frac{1}{x} = 2$ হলে $x^{3} + \frac{1}{x^{3}}$ এর মান কত ?

A. 1
B. 2
C. 3
D. 8

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Answer: Option B

Explanation:

দেওয়া আছে, a+ \frac{1}{a} =2 a^{3} + \frac{1}{a^{3}} = {(a + \frac{1}{a})}^{3} - 3 . a . \frac{1}{a} . (a + \frac{1}{a}) = 2^{3} - 3 \times 2 = 8 - 6 = 2

678 . $x + 2^{\frac{1}{3}} + 2^{\frac{2}{3}} = 0$ হলে, $x^{3} + 6$ এর মান কত?

A. 4x
B. 6x
C. 4
D. 8

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Answer: Option B

Explanation:

x + 2^{\frac{1}{3}} + 2^{\frac{2}{3}} = 0 b a, x = - (2^{\frac{1}{3}} + 2^{\frac{2}{3}}) b a, x^{3} = - \{{(2^{\frac{1}{3}} + 2^{\frac{2}{3}})}^{3}\} b a, x^{3} = - \{{(2^{\frac{1}{3}})}^{3} + {(2^{\frac{2}{3}})}^{3} + 3 . 2^{\frac{1}{3}} . 2^{\frac{2}{3}} . (2^{\frac{1}{3}} + 2^{\frac{2}{3}})\} b a, x^{3} = - \{2 + 4 + 3.2 . (- x)\} b a, x^{3} = - 6 + 6 x b a, x^{3} - 6 = 6 x

679 . $a^{2} + b^{2} + c^{2} + 2 a b - 2 b c$ এর সাথে কত যোগ করলে যোগফল পূর্ণবর্গ হবে ?

A. -2ab
B. 2bc
C. 2ca
D. -2ca

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Answer: Option D

Explanation:

680 . যদি a = 17 এবং b = 11 হয়, তবে $a^{2} - 2 a b + b^{2} =$ কত?

A. 36
B. 100
C. 289
D. 374

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Answer: Option A

Explanation:

681 . $x + \frac{1}{x} = 2$ হয়, তাহলে x এর মান কত?

A. 2
B. 1
C. $\frac{1}{2}$
D. $\frac{1}{4}$

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Answer: Option B

Explanation:

682 . $x + \frac{2}{x} = 3$ হলে, $x^{3} + \frac{8}{x^{3}}$ এর মান কত?

A. 1
B. 8
C. 9
D. 16

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Answer: Option C

Explanation:

683 . $2 (a^{2} + b^{2}) =$ কত?

A. ${(a + b)}^{2} - 2 a b$
B. ${(a + b)}^{2} + {(a - b)}^{2}$
C. ${(a - b)}^{2} + 2 a b$
D. ${(a + b)}^{2} - 4 a b$

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Answer: Option B

Explanation:

684 . a+b=4 এবং a-b=2 হলে, $a^{2} + b^{2}$ এর মান কত ?

A. 5
B. 10
C. 15
D. 20

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Answer: Option B

Explanation:

685 . x-y=3 এবং xy=10 হলে, ${(x + y)}^{2}$ এর মান--

A. 49
B. -29
C. -1

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Answer: Option A

Explanation:

(x + y)²

= (x - y)² + 4xy

= 3² + 4.10

= 9 + 40

= 49.

686 . If $2^{4 y} = 256$ , then $3^{y}$ equals :

A. 3
B. 8
C. 9
D. 10

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Answer: Option C

Explanation:

687 . x+y=2 $x^{2} + y^{2} = 4 x^{3} + y^{3}$ এর মান নির্ণয় করুন।

A. 4
B. 8
C. 12
D. 16

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Answer: Option B

Explanation:

688 . If $10^{2 y} = 25,$ then $10^{- y}$ equals:

A. $\frac{1}{50}$
B. $\frac{1}{625}$
C. $\frac{1}{2}$
D. $\frac{1}{5}$

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Answer: Option D

Explanation:

689 . $x^{2} + y^{2} + z^{2} = 4, x + y - z = 8$ এবং yz-zx-xy এর মান -

A. -60
B. -30
C. 30
D. 60

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Answer: Option B

Explanation:

690 . কোনটি অভেদ?

A. $x^{2} + 5 x + 6 = 0$
B. $a^{2} + 10 a + 9 = 0$
C. $4 x + 5 = 9$
D. ${(p + q)}^{2} = p^{2} + 2 p q + q^{2}$

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Answer: Option D

Explanation:

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