If x−1x=5, find the value of x3−1x3.
x−1x=5
Cubing both sides
(x−1x)3=(5)3⇒ x3−1x3−3(x−1x)=125⇒ x3−1x3−3×5=125⇒ x3−1x3−15=125⇒ x3−1x3=125+15=140∴ x3−1x3=140
If x+1x=5, find the value of x3+1x3.