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Find largest p for which inequalityin n variables hold.

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January 11, 2011
inequalitiesinequalities unsolved

Problem Statement

Find the largest positive real number pp (if it exists) such that the inequality x12+x22+⋯+xn2≥p(x1x2+x2x3+⋯+xn−1xn)x^2_1+ x_2^2+ \cdots + x^2_n\ge p(x_1x_2 + x_2x_3 + \cdots + x_{n-1}x_n) is satisfied for all real numbers xix_i, and (a)n=2;(b)n=5.(a) n = 2; (b) n = 5. Find the largest positive real number pp (if it exists) such that the inequality holds for all real numbers xix_i and all natural numbers n,n≥2.n, n \ge 2.
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