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Expansion of (x^2 - y^2)

If x^2 +...

Question

If $x^{2} + \frac{1}{x^{2}} = 38$ , find the value of $x - \frac{1}{x}$

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Solution

$x^{2} + \frac{1}{x^{2}} = 38$
we have,
$(x - \frac{1}{x})^{2} = x^{2} + \frac{1}{x^{2}} - 2$
$= 38 - 2$
$= 36$
$\Rightarrow x - \frac{1}{x} = \pm 6$

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