Question 100
Let $x, y, z$ be positive numbers such that $x^2y^2 + y^2z^2 + z^2x^2 = 6xyz$. Prove that
$$
\sqrt{\frac{x}{x + yz}} + \sqrt{\frac{y}{y + zx}} + \sqrt{\frac{z}{z + xy}} \ge \sqrt{3}
$$
$$
\sqrt{\frac{x}{x + yz}} + \sqrt{\frac{y}{y + zx}} + \sqrt{\frac{z}{z + xy}} \ge \sqrt{3}
$$