Question

if x=√2-1, find (x-1/x)³

Answer 1

Heya!!

Thanks for asking the question .

Pls refer to the attachment above.

Answer : -8

Hope it helps you : )

Answer 2

Given,

$x = \sqrt{2} - 1 \\ \\ \frac{1}{x} = \frac{1}{\sqrt{2} - 1} \\ \\ \frac{1}{x} = \frac{\sqrt{2}+1}{(\sqrt{2} - 1)(\sqrt{2} + 1)} \\ \\ \frac{1}{x} = \frac{\sqrt{2} + 1}{2 - 1} \\ \\ \frac{1}{x} = \sqrt{2} + 1 \\ \\ (x - \frac{1}{x})^{3} = (\sqrt{2} -1 -\sqrt{2} -1 )^{3} \\ \\ = (-2)^{3} \\ \\ = -8 \ \ \textbf{Ans.}$