Question

Solve:
$x^5+242=\frac{243}{x^5}$.

Answer 1

$x^5+242=\frac{243}{x^5}$

Let $x^5=z$

Then $z+242=\frac{243}{z}$

$⟹z^2+242z-243=0$

$⟹(z-1)(z+243)=0$

So, $z=1$ or $Z=-243$

$⟹x^5=1⟹x=1$

or

$⟹x^5=-243⟹x^5=(-3{)}^5⟹x=-3$

$\therefore x=1,-3$