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Question Number 28143 by ktomboy1992 last updated on 21/Jan/18

$$\mathrm{x}-\frac{1}{\mathrm{x}}=3$$$${\mathrm{x}}^2-\frac{1}{{\mathrm{x}}^2}=?$$

Answered by mrW2 last updated on 21/Jan/18

$${(x-\frac{1}{x})}^2=9$$$$x^2-2+\frac{1}{x^2}=9$$$$x^2+2+\frac{1}{x^2}=13$$$${(x+\frac{1}{x})}^2=13$$$$x+\frac{1}{x}=\pm \sqrt{13}$$$${\mathrm{x}}^2-\frac{1}{{\mathrm{x}}^2}=(x+\frac{1}{x})(x-\frac{1}{x})=\pm 3\sqrt{13}$$

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