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Solving a Quadratic Equation by Completion of Squares Method

If, x-1x=5 ...

Question

If, $x - \frac{1}{x} = 5$ , Solve: $x^{2} + \frac{1}{x^{2}}$ .

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Solution

We know that,

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

$⟹ {(x - \frac{1}{x})}^{2} = 5^{2}$

$⟹ x^{2} + \frac{1}{x^{2}} - 2 = 25$

$⟹ x^{2} + \frac{1}{x^{2}} = 27$

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