Assume that x1,…,xn≥−1x_1, \dots, x_n \ge -1x1,…,xn≥−1 and ∑i=1nxi3=0\sum\limits_{i=1}^{n} x_i^3 = 0i=1∑nxi3=0. Prove that ∑i=1nxi≤n3\sum\limits_{i=1}^{n} x_i \le \dfrac{n}{3}i=1∑nxi≤3n.
Hidden so you can work on the problem first.