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Expression Formation

If x2 + 1 x...

Question

If $x^{2} + \frac{1}{x^{2}} = 51,$ find $x - \frac{1}{x}$

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Solution

solution :-
$x^{2} + \frac{1}{x^{2}} = 51$

Now $(x - \frac{1}{x})^{2} = x^{2} + \frac{1}{x^{2}} - 2 \times x \times \frac{1}{x}$

$= 51 - 2$

$= 49$

$\Rightarrow x - \frac{1}{x} = \pm 7$

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