Question 185
Given $a \gt b \gt c \gt 0$, prove that
$$
a^{4} b + b^{4} c + c^{4} a \gt a b^{4} + b c^{4} + c a^{4}.
$$
$$
a^{4} b + b^{4} c + c^{4} a \gt a b^{4} + b c^{4} + c a^{4}.
$$
MathNet 2026 — Part 09 Question 185
Math Olympiad Vault · MathNet 2026 — Part 09