Question 107
For nonnegative reals $x, y, z \ge 0$ satisfying $xy + yz + zx = 3$, prove
$$
(1 + 2x)(1 + y)^2 + (1 + 2y)(1 + z)^2 + (1 + 2z)(1 + x)^2 \ge 36.
$$
$$
(1 + 2x)(1 + y)^2 + (1 + 2y)(1 + z)^2 + (1 + 2z)(1 + x)^2 \ge 36.
$$
MathNet 2022-part-03 — 197 problems (EN–VI) Question 107
Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)