Question

X = 1 + root 2 , find the value of (x - 1/x )^3​

Answer 1

Answer:

$(\sqrt{2})^3$

Step-by-step explanation:

Given the expression

$(x - \frac{1}{x} )^3$

Simplify

$(\frac{x^2-x}{x} )^3$

Given that x = 1+√2

Substitute

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