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(a-b)^2 Expansion and Visualisation

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Question

If ${(x - \frac{1}{x})}^{2} = 81$ , find the value of $x^{2} + \frac{1}{x^{2}}$ .

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Solution

$(x - \frac{1}{x})^{2} = 81$

$x^{2} + \frac{1}{x^{2}} - 2 = 81$

$x^{2} + \frac{1}{x^{2}} = 83$

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