Question

if x = 1-squareroot of 2, find the value of (x-1/x)power of 3

Answer 1

first of all:
(x - 1/x)^3 = x^3 - 3x + 3/x - 1/x^3

so we will need x^3

if x = 1 - √2, then
x^3
= (1-√2)^3
= 7-5√2 , I will leave it up to you to expand it

So we have :
(7 - 5√2) - 3(1 - √2) + 3/(1 - √2) - 1/(7 - 5√2)

rationalize the last two terms and simplify
Let me know what you got