KöMaL 2015 A642

Let $n\ge3$, let $x_1,\ldots,x_n$ be nonnegative numbers, and let $A=\sum_{i=1}^n x_i$, $B= \sum_{i=1}^n x_i^2$ and $C= \sum_{i=1}^n x_i^3$. Prove that $(n+1)A^2B + (n-2)B^2 \ge A^4 + (2n-2)AC$ .