If x-1-x-20- then the value of x 2-1- x 2 isA- 402B- 398C- 395D- 405

The correct option is B 398Given that, x +1/x = 20 Squaring on both sides, ⇒ (x +1/x)^2 = (20)^2 = 400 nbsp;Using the identity (a + b)^2 = a^2 + b^2 + 2ab, x ...

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Standard VIII

Mathematics

Algebraic Quadratic Identity

If x+1/x=20, ...

Question

If $x + \frac{1}{x} = 20$ , then the value of
$x^{2} + \frac{1}{x^{2}}$ is .

402

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398

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395

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405

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Solution

The correct option is B 398
Given that,
$x + \frac{1}{x} = 20$
Squaring on both sides,
$\Rightarrow (x + \frac{1}{x})^{2} = (20)^{2} = 400$
Using the identity $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ,
$x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x} = 400$
$\Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 400$
$\Rightarrow x^{2} + \frac{1}{x^{2}} = 400 - 2 = 398$

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If x+1x=20, then the value of x2+1x2 is .

The correct option is B 398Given that, x+1x=20 Squaring on both sides, ⇒(x+1x)2=(20)2=400 Using the identity (a+b)2=a2+b2+2ab, x2+1x2+2×x×1x=400 ⇒x2+1x2+2=400 ​​⇒x2+1x2=400−2=398

If $x + \frac{1}{x} = 20$ , then the value of
$x^{2} + \frac{1}{x^{2}}$ is .