Question 49
Let $a, b, c$ be positive real numbers such that $a^{3}+b^{3}=c^{3}$. Prove that
$$
a^{2}+b^{2}-c^{2} \gt 6(c-a)(c-b)
$$
$$
a^{2}+b^{2}-c^{2} \gt 6(c-a)(c-b)
$$
MathNet 2009-part-02 — 175 problems (EN–VI) Question 49
Math Olympiad Vault · MathNet 2009-part-02 — 175 problems (EN–VI)