Question 104
Suppose $x, y, z$ are positive numbers such that $x + y + z = 1$. Prove that
$$
(a) \ xy + yz + zx \geq 9xyz;
$$
$$
(b) \ xy + yz + zx \lt \frac{1}{4} + 3xyz.
$$
$$
(a) \ xy + yz + zx \geq 9xyz;
$$
$$
(b) \ xy + yz + zx \lt \frac{1}{4} + 3xyz.
$$