Question 118
Let $a, b, c \ge 0$ be non-negative numbers satisfying $a^3 + b^3 + c^3 = abc + 2$. Prove that
$$
a^4 + b^4 + c^4 \ge a + b + c.
$$
$$
a^4 + b^4 + c^4 \ge a + b + c.
$$
MathNet 2024-part-03 — 168 problems (EN–VI) Question 118
Math Olympiad Vault · MathNet 2024-part-03 — 168 problems (EN–VI)