Question 25
Let $x$, $y$, $z$ be positive real numbers satisfying $x + y + z + xyz = 4$. Show that
$$
\frac{x}{\sqrt{2y+3z}} + \frac{y}{\sqrt{2z+3x}} + \frac{z}{\sqrt{2x+3y}} \ge \frac{1}{\sqrt{5}}(x+y+z).
$$
$$
\frac{x}{\sqrt{2y+3z}} + \frac{y}{\sqrt{2z+3x}} + \frac{z}{\sqrt{2x+3y}} \ge \frac{1}{\sqrt{5}}(x+y+z).
$$