Question

If
$x + \frac{1}{x } = 7 \: then \: find \: the \: value \: of \: {x}^{2 \: } \: + \frac{1}{x 2 }$

Answer 1

Hey mate !


Given :)

$\mathsf{x + \frac{1}{x} = 7}$


Now,

On squaring both sides.


$\mathsf{(x + \frac{1}{x} ) {}^{2} = (7) {}^{2} } \\ \\ \mathsf{ \implies x {}^{2} + \frac{1}{x {}^{2} } + 2 = 49} \\ \\ \mathsf{ \implies x {}^{2} + \frac{1}{x {}^{2} } = 49 - 2} \\ \\ \mathsf{ \implies x {}^{2} + \frac{1}{x {}^{2} } = 47}$

Thanks for the question !

Answer 2

Hi there !

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• Given :

x + 1 / x = 7  

• To find :

Value of x² + 1 / x².

• Solution : 

x + 1 / x = 7

On squaring both sides :)

( x + 1 / x )² = (7)²

⇒ x² + 1 / x² + 2 = 49

⇒ x² + 1 / x² = 49 - 2

⇒ x² + 1 / x² = 47

Hence,

The answer is ⇒ x² + 1 / x² = 47

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Thanks for the question !