x−(1/x)=4 then x^2 −(1/x^2 )=?


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Question Number 165060 by mathlove last updated on 25/Jan/22

$x - \frac{1}{x} = 4 t h e n x^{2} - \frac{1}{x^{2}} = ?$
	Answered by TheSupreme last updated on 25/Jan/22

	$x^{2} + \frac{1}{x^{2}} = 18$ ${(x + \frac{1}{x})}^{2} = x^{2} + \frac{1}{x^{2}} + 2 = 20$ $(x + \frac{1}{x}) = \sqrt{20} = \pm 2 \sqrt{5}$ $(x - \frac{1}{x}) (x + \frac{1}{x}) = \pm 8 \sqrt{5}$ $g e n e r a l$ $(x - \frac{1}{x}) = t$ $x^{2} + \frac{1}{x^{2}} - 2 = t^{2}$ $(x^{2} + \frac{1}{x^{2}}) = t^{2} + 2$ ${(x + \frac{1}{x})}^{2} = t^{2} + 2 + 2 = t^{2} + 4$ $(x^{2} - \frac{1}{x^{2}}) = \pm t \sqrt{t^{2} + 4}$
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