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Question

If x=1-√2, then find the value of (x-1/x)³

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Solution

x=1-√2
1/x=1/(1-√2)

=1/(1-√2) * (1+√2)/(1+√2)

=1+√2/(1^2- √2^2)

=1+√2/ (1-2)

=-(1+√2)

X - (I/X) =1-√2 - -(1+√2)

= 1-√2 +1+√2
= 2
(X - 1/X)3 = 2^3 =8

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