Question

If x -1/x = 10 , Find the value of x^2 +1/x^2

Answer 1

Given :-

• x - 1/x = 10

To Find :-

• value of x² + 1/x²

Solution :-

we have,

$\bold{x - \frac{1}{x} = 10}$

on squaring both sides;

$\bold{: \implies \bigg( {x - \frac{1}{x} \bigg)}^{2} = {10}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times \cancel x \times \frac{1}{ \cancel x} = 100 } \\ \\ \bold{: \implies {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 100 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies {x}^{2} + \frac{1}{ {x}^{2} } = 100 + 2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \boxed{ \bold{{x}^{2} + \frac{1}{ {x}^{2} } = 102 }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, value of x² + 1/x² is 102