parmenides51 wrote: Prove that for any reals $a> b> c$, the inequality $a^2(b - c) + b^2(c - a) + c^2(a - b)> 0$. $$a^2(b - c) + b^2(c - a) + c^2(a - b)=(a-b)(b-c)(a-c)> 0$$