A Cyclic Sum With a Twist

Problem

Let $a, b, c > 0$ . Prove that

\frac{a\left(a^2+bc\right)}{b+c} + \frac{b\left(b^2+ca\right)}{c+a} + \frac{c\left(c^2+ab\right)}{a+b} \ge ab + bc + ca.

Answer

Solution

Difficulty	7/10
Topics	Polynomials, inequality, Symmetry

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