Question 138
Suppose $0 \le x, y, z$, and $x+y+z \le 1$. Prove that
$$
6xyz \le x(1-x) + y(1-y) + z(1-z),
$$
and describe the cases of equality.
$$
6xyz \le x(1-x) + y(1-y) + z(1-z),
$$
and describe the cases of equality.
MathNet 2026 — Part 05 Question 138
Math Olympiad Vault · MathNet 2026 — Part 05