Question

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

Answer 1

`(√(2))^3`

Explanation:

Given the expression

`(x - (1)/(x) )^3`

Simplify

`((x^2-x)/(x) )^3`

Given that x = 1+√2

Substitute

`(((1+√(2) )^2-(1+√(2) ))/(1+√(2) ) )^3\\=( (1+2√(2) +2 - 1 - √(2))/(1+√(2)) )^3\\= ((√(2)+2)/(1+√(2)))^3 \\Rationalize\\= ((√(2)-2+2-2√(2))/(1-2))^3 \\=( (-√(2))/(-1))^3 \\= (√(2))^3\\ \\`