Question 44
Let $x$, $y$, $z$ and $a$, $b$, $c$ be positive real numbers such that $x + y + z = a + b + c$ and $xyz = abc$. Suppose $\max\{x, y, z\} \ge \max\{a, b, c\}$. Prove that
$$
ab + bc + ca \ge xy + yz + zx.
$$
$$
ab + bc + ca \ge xy + yz + zx.
$$