Question 82
For all positive real numbers $x$, $y$ and $z$ prove the following inequality
$$
\frac{x^2}{xy+z} + \frac{y^2}{yz+x} + \frac{z^2}{zx+y} \ge \frac{(x+y+z)^3}{3[x^2(y+1) + y^2(z+1) + z^2(x+1)]}.
$$
$$
\frac{x^2}{xy+z} + \frac{y^2}{yz+x} + \frac{z^2}{zx+y} \ge \frac{(x+y+z)^3}{3[x^2(y+1) + y^2(z+1) + z^2(x+1)]}.
$$