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China Mathematical Olympiad 2017 Q6

Source: China Mathematical Olympiad 2017, Problem 6

November 24, 2016
BPSQChinaPRCinequalitiesInequality proposedconvex-concave inequalitiessqing orz

Problem Statement

Given an integer n≥2n \geq2 and real numbers a,ba,b such that 0<a<b0<a<b. Let x1,x2,…,xn∈[a,b]x_1,x_2,\ldots, x_n\in [a,b] be real numbers. Find the maximum value of x12x2+x22x3+⋯+xn−12xn+xn2x1x1+x2+⋯+xn−1+xn.\frac{\frac{x^2_1}{x_2}+\frac{x^2_2}{x_3}+\cdots+\frac{x^2_{n-1}}{x_n}+\frac{x^2_n}{x_1}}{x_1+x_2+\cdots +x_{n-1}+x_n}.
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