Question

If x=1-√2 then (x-1/x)^3=
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Answer 1

Answer:

x=1-√2

1/x=1/(1-√2)

=(1+√2)/(1-√2)(1+√2)

=(1+√2)/{(1)^2-(√2)^2}

=(1+√2)/((1-2)

=(1+√2)/-1

= -(1+√2)

so,

(x-1/x)^3

={(1-√2)-.-(1+√2)}^3

=(1-√2+1+√2)^3

=(2)^3

=8