Question 144
Let $x$, $y$, $z$ be positive real numbers satisfy the condition $x^{2} + y^{2} + z^{2} = 2(xy + yz + zx)$. Prove that
$$
x + y + z + \frac{1}{2xyz} \geq 4
$$
$$
x + y + z + \frac{1}{2xyz} \geq 4
$$
MathNet 2016-part-04 — 184 problems (EN–VI) Question 144
Math Olympiad Vault · MathNet 2016-part-04 — 184 problems (EN–VI)