If x=2-√3,then What is the value of x cube - 1/x cube?

1 Answer
Mar 26, 2018

x³-1/(x^3)=-30sqrt(3)

Explanation:

[0]x=2-sqrt3
[1] x³=(2-sqrt3)³
[2] x³=8-12*sqrt(3)+18-3*sqrt(3)=26-15sqrt3
[3] -1/(x^3)=-1/(26-15*sqrt(3))=-(26+15sqrt(3))
So:
[4]x³-1/(x^3)=26-15sqrt(3)-26-15sqrt(3)=-30sqrt(3)
\0/ here's our answer !