Question 6
If $x, y, z \gt 0$ with $x^2y^2 + y^2z^2 + z^2x^2 = 6x^2y^2z^2$, prove that:
$$
\sqrt{\frac{x}{x+yz}} + \sqrt{\frac{y}{y+zx}} + \sqrt{\frac{z}{z+xy}} \ge \sqrt{3}.
$$
$$
\sqrt{\frac{x}{x+yz}} + \sqrt{\frac{y}{y+zx}} + \sqrt{\frac{z}{z+xy}} \ge \sqrt{3}.
$$