MathNet 2026 — Part 03 Question 51

Proof of positive real numbers $x, y, z$ with $x+y+z=1$ The following inequality: $$
\frac{x^{2}+y^{2}}{z}+\frac{y^{2}+z^{2}}{x}+\frac{z^{2}+x^{2}}{y} \geq 2
$$