Question

if x = 1-square root of 2, find the value of (x - 1/x) power of 2

Answer 1

x = 1 - √2 ,

then x^2 = 1 - 2√2 + 2
= 3 - 2√2

then (x - 1/x)^2
= x^2 - 2 + 1/x^2
= 3-2√2 - 2 + 1/(3-2√2)
= ....

rationalizing 1/(3-2√2)

1/(3-2√2)
=1/(3-2√2 * (3+2√2)/(3+2√2)
= (3+2√2)/1
so back in ...
= 3 - 2√2 - 2 + 3+2√2
= 4