Question

2. If x= 1 + √2 then
show that:(x-1/x)³=8​

Answer 1

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