Question

If $x^4+\frac{1}{x^4}=6239$, find $x+\frac{1}{x}$.

Answer 1

$x^4+\frac{1}{x^4}=6239$

$\Rightarrow {(x^2+\frac{1}{x^2})}^2-2=6239$

$\Rightarrow x^2+\frac{1}{x^2}=\sqrt{6239+2}$

$\Rightarrow x^2+\frac{1}{x^2}=\sqrt{6241}=79$

$\Rightarrow {(x+\frac{1}{x})}^2-2=79$

$\Rightarrow x+\frac{1}{x}=\sqrt{79+2}=\sqrt{81}=9$