Question 39
Let $x$, $y$ and $z$ be positive real numbers such that $xyz = 3(x + y + z)$. Show that
$$
\frac{1}{x^2(y+1)} + \frac{1}{y^2(z+1)} + \frac{1}{z^2(x+1)} \geq \frac{3}{4(x+y+z)}
$$
and determine the cases of equality.
$$
\frac{1}{x^2(y+1)} + \frac{1}{y^2(z+1)} + \frac{1}{z^2(x+1)} \geq \frac{3}{4(x+y+z)}
$$
and determine the cases of equality.