Question 34
Let $x$, $y$, and $z$ be positive real numbers. Prove that
$$
\frac{2x^2 + xy}{(y + \sqrt{zx} + z)^2} + \frac{2y^2 + yz}{(z + \sqrt{xy} + x)^2} + \frac{2z^2 + zx}{(x + \sqrt{yz} + y)^2} \geq 1.
$$
$$
\frac{2x^2 + xy}{(y + \sqrt{zx} + z)^2} + \frac{2y^2 + yz}{(z + \sqrt{xy} + x)^2} + \frac{2z^2 + zx}{(x + \sqrt{yz} + y)^2} \geq 1.
$$