Problem

Source: Iran MO 3rd round 2019 mid-terms - Algebra P1

Tags: inequalities, Iran



$a,b$ and $c$ are positive real numbers so that $\sum_{\text{cyc}} (a+b)^2=2\sum_{\text{cyc}} a +6abc$. Prove that $$\sum_{\text{cyc}} (a-b)^2\leq\left|2\sum_{\text{cyc}} a -6abc\right|.$$