IMO-ulikhet

[Gustav]

La $x,y,z$ være positive reelle tall slik at $xyz\geq 1$. Vis at
\begin{equation*}
\frac{x^5-x^2}{x^5+y^2+z^2}+\frac{y^5-y^2}{y^5+z^2+x^2}+\frac{z^5-z^2}{z^5+x^2+y^2}\geq 0
\end{equation*}