Question

If $x+\frac{1}{x}=3$, then find the value of $x^6+\frac{1}{x^6}$.

Answer 1

We have to find the value of

Given

Using identity

Here

By substituting the value of We get,

By transposing + 2 to left hand side, we get

Cubing on both sides we get,

Using identity ${\left(a+b\right)}^3=a^3+b^3+3ab\left(a+b\right)$

Here

Put we get

By transposing 21 to left hand side we get ,

Hence the value of is .