Question 106
Suppose $a$, $b$, $c$ are real numbers such that $a + b + c = 1$. Prove that
$$
a^3 + b^3 + c^3 + 3(1-a)(1-b)(1-c) = 1.
$$
$$
a^3 + b^3 + c^3 + 3(1-a)(1-b)(1-c) = 1.
$$
MathNet 2026 — Part 06 Question 106
Math Olympiad Vault · MathNet 2026 — Part 06