Question

If $x+\frac{1}{x}=9$, then the value of $x^4+\frac{1}{x^4}$ is equal to __

Answer 1

Answer: 6239

$x+\frac{1}{x}=9$
Squaring both sides,
${\left(x+\frac{1}{x}\right)}^2=81$
$\Rightarrow x^2+\frac{1}{x^2}+2x^2\frac{1}{x^2}=81$
$\Rightarrow x^2+\frac{1}{x^2}=79$
Squaring again on both sides,
${\left(x^2+\frac{1}{x^2}\right)}^2=6241$
$\Rightarrow x^4+\frac{1}{x^4}+2\cdot \frac{1}{x^2}\cdot x^2=6241$
$\Rightarrow x^4+\frac{1}{x^4}=6239$