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

1 Answer
Guillaume L.
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 !

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