Question

If $x+\frac{1}{x}=3$, Find the value of $x^4+\frac{1}{x^4}$.

Answer 1

Squaring both sides of the equation,

$x^2+\frac{1}{x^2}+2=9$

Hence,

$x^2+\frac{1}{x^2}=9-2=7$

Squaring the above equation .

$x^4+\frac{1}{x^4}+2=49x^4+\frac{1}{x^4}=47$