MathDB
Inequality

Source: Vietnam NMO 1986 Problem 1

February 6, 2009
inequalitiesfunctioninequalities unsolved

Problem Statement

Let 12≤a1,a2,…,an≤5 \frac{1}{2}\le a_1, a_2, \ldots, a_n \le 5 be given real numbers and let x1,x2,…,xn x_1, x_2, \ldots, x_n be real numbers satisfying 4x_i^2\minus{} 4a_ix_i \plus{} \left(a_i \minus{} 1\right)^2 \le 0. Prove that \sqrt{\sum_{i\equal{}1}^n\frac{x_i^2}{n}}\le\sum_{i\equal{}1}^n\frac{x_i}{n}\plus{}1
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