If x-1-x-10 and x-0- then x2-1-x2-A- 102B- 98C- 10D- 100

The correct option is B 98Given that, x + 1/x = 10 nbsp;(x + 1/x)^2 =100 Using the identity, (a+b)^2 = a^2+b^2+2ab, we have nbsp;(x + 1/x)^2 = x^2 + 1/ ...

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Standard X

Mathematics

Algebraic Identities

If x+1/x=10 a...

Question

If $x + \frac{1}{x} = 10$ and $x \neq 0$ , then $x^{2} + \frac{1}{x^{2}}$ = ___.

102

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100

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Solution

The correct option is B 98
Given that, $x + \frac{1}{x} = 10 ⟹ (x + \frac{1}{x})^{2} = 100$

Using the identity,

$(a + b)^{2} = a^{2} + b^{2} + 2 a b$ , we have

$(x + \frac{1}{x})^{2} = x^{2} + \frac{1}{x^{2}} + 2 (x) (\frac{1}{x})$
$⟹ 100 = x^{2} + \frac{1}{x^{2}} + 2$
$⟹ x^{2} + \frac{1}{x^{2}} = 100 - 2$
$∴ x^{2} + \frac{1}{x^{2}} = 98$

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If x+1x=10 and x≠0, then x2+1x2 = ___.

The correct option is B 98Given that, x+1x=10⟹(x+1x)2=100 Using the identity, (a+b)2=a2+b2+2ab, we have (x+1x)2=x2+1x2+2(x)(1x) ⟹100=x2+1x2+2 ⟹x2+1x2=100−2 ∴x2+1x2=98

If $x + \frac{1}{x} = 10$ and $x \neq 0$ , then $x^{2} + \frac{1}{x^{2}}$ = ___.