Question

If x=1-root 2 what will be the value of (x-1/x)^3???

Answer 1

Hello Mate!

$x = 1 - \sqrt{2} \\ \frac{1}{x} = \frac{1}{1 - \sqrt{2} } \\ \frac{1}{1 - \sqrt{2} } \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} } = \\ \frac{1 + \sqrt{2} }{ - 1} = \sqrt{2} - 1 \\ {( x - \frac{1}{x}) }^{3} = {(1 - \sqrt{2} - \sqrt{2} + 1}^{3} \\ {(2 - 2 \sqrt{2} )}^{3} \\ 8 - 16 \sqrt{2} + 48 - 24 \sqrt{2} \\ 56 - \sqrt{2} (24 + 16) \\ 56 - 40 \sqrt{2}$

Hope it helps☺!