Question

find the value of (x -1/x)cube if x =1 + root 2

Answer 1

1/X=1/1+√2
=1*1-√2/1+√2*1-√2
=1-√2/1²-√2²
=1-√2/1-2
=1-√2/-1
=-1+√2
(1+√2-(-1+√2))³
(1+√2+1-√2)³
(2)³
8

Answer 2

put value of x in equation
=($\sqrt{2}$-1+1)/$\sqrt{2}$+1
=root 2/(1+root2)
rationalise the denominator by multiplying it with (1-root2) with numerator and denominator
=(2-root2)$^{3}$
now apply the identity (a-b)cube=acube-bcube+3ab(a-b)