Problem

Source:  Iran 3rd round-2017-Algebra final exam-P3

Tags: algebra, Inequality, AM-GM, Iran, inequalities



Let $a,b$ and $c$ be positive real numbers. Prove that $$\sum_{cyc} \frac {a^3b}{(3a+2b)^3} \ge \sum_{cyc} \frac {a^2bc}{(2a+2b+c)^3} $$