Question

if x= 1- root 2, find the value of (x-1/x) cube​

Answer 1

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