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Maximal value of |x_k|

Source: Chinese Mathematical Olympiad 1998 Problem 6

August 22, 2013
inequalities unsolvedinequalities

Problem Statement

Let x1,x2,…,xnx_1,x_2,\ldots ,x_n be real numbers, where n≥2n\ge 2, satisfying ∑i=1nxi2+∑i=1n−1xixi+1=1\sum_{i=1}^{n}x^2_i+ \sum_{i=1}^{n-1}x_ix_{i+1}=1 . For each kk, find the maximal value of ∣xk∣|x_k|.
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