Question 88
The real numbers $x$, $y$, $z$, $m$, $n$ are positive, such that $m+n \geq 2$. Prove that
$$
\begin{gathered}
x \sqrt{y z(x+m y)(x+n z)}+y \sqrt{x z(y+m x)(y+n z)}+z \sqrt{x y(z+m x)(z+n y)}
\\
\leq \frac{3(m+n)}{8}(x+y)(y+z)(z+x)
\end{gathered}
$$
$$
\begin{gathered}
x \sqrt{y z(x+m y)(x+n z)}+y \sqrt{x z(y+m x)(y+n z)}+z \sqrt{x y(z+m x)(z+n y)}
\\
\leq \frac{3(m+n)}{8}(x+y)(y+z)(z+x)
\end{gathered}
$$