Answer:
[tex](\sqrt{2})^3[/tex]
Step-by-step explanation:
Given the expression
[tex](x - \frac{1}{x} )^3[/tex]
Simplify
[tex](\frac{x^2-x}{x} )^3[/tex]
Given that x = 1+√2
Substitute
[tex](\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\\ \\[/tex]
