Question 132
Positive real numbers $x$, $y$, and $z$ satisfy the inequality $xyz \ge xy + yz + zx$. Prove that
$$
\sqrt{xyz} \ge \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$
$$
\sqrt{xyz} \ge \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$
MathNet 2016-part-04 — 184 problems (EN–VI) Question 132
Math Olympiad Vault · MathNet 2016-part-04 — 184 problems (EN–VI)