Question 42
For all $x, y, z \gt 0$ satisfying $\frac{x}{yz} + \frac{y}{zx} + \frac{z}{xy} \le x + y + z$, prove that
$$
\frac{1}{x^2 + y + z} + \frac{1}{y^2 + z + x} + \frac{1}{z^2 + x + y} \le 1.
$$
$$
\frac{1}{x^2 + y + z} + \frac{1}{y^2 + z + x} + \frac{1}{z^2 + x + y} \le 1.
$$