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# help with algebra

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If $$x^2 + \frac{1}{x^2} = 171$$, then find all possible values of $$x - \frac{1}{x}$$

Jul 13, 2020

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Let $$t = x - \dfrac1x$$.

$$t^2 + 2 = x^2 + \dfrac1{x^2} = 171$$

$$t^2 = 169$$

$$t = \pm 13$$

$$x - \dfrac1x = \pm13$$

Therefore there are two possible values.

Jul 13, 2020