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maxima of xi^2

Source: Romanian TST 2018 Day 1 Problem 1

May 25, 2020
inequalitiesn-variable inequality

Problem Statement

Find the least number c c satisfyng the condition ∑i=1nxi2≤cn\sum_{i=1}^n {x_i}^2\leq cn and all real numbers x1,x2,...,xnx_1,x_2,...,x_n are greater than or equal to −1-1 such that ∑i=1nxi3=0\sum_{i=1}^n {x_i}^3=0
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