Question 92
Let $x, y, z$ be three positive real numbers such that $x^2 + y^2 + z^2 + 3 = 2(xy + yz + zx)$. Prove that
$$
\sqrt{xy} + \sqrt{yz} + \sqrt{zx} \geq 3.
$$
$$
\sqrt{xy} + \sqrt{yz} + \sqrt{zx} \geq 3.
$$
MathNet 2017-part-05 — 176 problems (EN–VI) Question 92
Math Olympiad Vault · MathNet 2017-part-05 — 176 problems (EN–VI)