MathNet 2025 — Part 01 (100 complete bilingual questions) Question 97

Non-negative real numbers $x$, $y$, $z$ satisfy the relations $xy + 4 \le 2(x+z)$, $yz + 4 \le 2(y+x)$, $zx + 4 \le 2(z+y)$. Prove that $x = y = z$.