Question 104
Let $x, y, z$ be positive real numbers satisfying $x + y + z = 1$. Find the smallest real number $k$ such that the inequality
$$
\frac{x^2 y^2}{1-z} + \frac{y^2 z^2}{1-x} + \frac{z^2 x^2}{1-y} \le k - 3xyz
$$
always holds.
$$
\frac{x^2 y^2}{1-z} + \frac{y^2 z^2}{1-x} + \frac{z^2 x^2}{1-y} \le k - 3xyz
$$
always holds.