Question 143
Given $x$, $y$, $z \in (0, 1)$ satisfying
$$
\sqrt{\frac{1-x}{yz}} + \sqrt{\frac{1-y}{zx}} + \sqrt{\frac{1-z}{xy}} = 2,
$$
find the maximum value of $xyz$. (Posed by Tang Lihua)
$$
\sqrt{\frac{1-x}{yz}} + \sqrt{\frac{1-y}{zx}} + \sqrt{\frac{1-z}{xy}} = 2,
$$
find the maximum value of $xyz$. (Posed by Tang Lihua)