Question 17
Let $a$, $b$, $c$ be the side lengths of a triangle. Prove that
$$
2 (a^3 + b^3 + c^3) \lt (a + b + c) (a^2 + b^2 + c^2) \le 3 (a^3 + b^3 + c^3).
$$
$$
2 (a^3 + b^3 + c^3) \lt (a + b + c) (a^2 + b^2 + c^2) \le 3 (a^3 + b^3 + c^3).
$$
MathNet 2026 — Part 06 Question 17
Math Olympiad Vault · MathNet 2026 — Part 06