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Algebraic Identities

If x2+1/x2=66...

Question

If $x^{2} + \frac{1}{x^{2}} = 66,$ find the value of $x - \frac{1}{x}$ .

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Solution

$x^{2} + \frac{1}{x^{2}} = 66 {(x - \frac{1}{x})}^{2} = x^{2} + \frac{1}{x^{2}} - 2 = 66 - 2 = 64 = (\pm 8)^{2} ∴ x - \frac{1}{x} = \pm 8$

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