Question

(x+1/x)^2=3 show that ( x ^ 3 + 1 / x ^ 3)=0

Answer 1

It's quite simple
(x+1/x)^2=3 then (x+1/x) = √3
Since power 2 goes from lbs to rhs
( x ^ 3 + 1 / x ^ 3) = (x + 1/x )^3 - 3(x + 1/x )
Here we know the value of x +1/x = √3 which we had already founded
Now replace this value.
We get,
(√3)^3 - 3√3
Therefore, 3√3 - 3√3 = 0
Hence proved