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China Mathematical Olympiad 1992 problem2

Source: China Mathematical Olympiad 1992 problem2

September 30, 2013
inequalitiesquadraticsinequalities unsolved

Problem Statement

Given nonnegative real numbers x1,x2,…,xnx_1,x_2,\dots ,x_n, let a=min{x1,x2,…,xn}a=min\{x_1, x_2,\dots ,x_n\}. Prove that the following inequality holds: \sum^{n}_{i=1}\dfrac{1+x_i}{1+x_{i+1}}\le n+\dfrac{1}{(1+a)^2}\sum^{n}_{i=1}(x_i-a)^2    (x_{n+1}=x_1), and equality occurs if and only if x1=x2=⋯=xnx_1=x_2=\dots =x_n.
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