Question 64
If $x$, $y$, $z$ are positive real numbers with sum $12$, prove that:
$$
\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + 3 \ge \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$
When is equality valid?
$$
\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + 3 \ge \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$
When is equality valid?