Question 33
Let $x, y, z$ be positive real numbers with $x + y + z \ge 3$. Prove that
$$
\frac{1}{x+y+z^2} + \frac{1}{y+z+x^2} + \frac{1}{z+x+y^2} \le 1
$$
$$
\frac{1}{x+y+z^2} + \frac{1}{y+z+x^2} + \frac{1}{z+x+y^2} \le 1
$$
MathNet 2015-part-01 — 191 problems (EN–VI) Question 33
Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)