Question 33
Let $x, y, z$ be three non-negative real numbers such that $x \leqslant 1$. Prove that:
$$
x y + y + 2 z \geqslant 4 \sqrt{x y z}
$$
$$
x y + y + 2 z \geqslant 4 \sqrt{x y z}
$$
MathNet 2023-part-02 — 191 problems (EN–VI) Question 33
Math Olympiad Vault · MathNet 2023-part-02 — 191 problems (EN–VI)