If $x - \frac{1}{x} = \sqrt{5}$, find the value of $x^2 + \frac{1}{x^2}$

Given :

The given term is $x - \frac{1}{x} = \sqrt{5}$

To find:

We have to find the value of  $x^2 + \frac{1}{x^2}$.

Solution:

$x - \frac{1}{x} = \sqrt{5}$.

Squaring on both sides, we get

$(x - \frac{1}{x})^2 = (\sqrt{5})^2$

$x^2 -2(x)(\frac{1}{x}) + (\frac{1}{x})^2 = 5$.

$x^2 - 2 + \frac{1}{x^2} = 5$.

$x^2 + \frac{1}{x^2} = 5 + 2$

$x^2 + \frac{1}{x^2} = 7$

Therefore, the value of $x^2 + \frac{1}{x^2}$ is $7$.

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Updated on: 10-Oct-2022

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