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Maximum value of cyclic expression

Source: Romania TST 2 2012, Problem 4

May 10, 2012
algebrafunctiondomaininequalitiesinequalities proposedBalkan

Problem Statement

Let kk be a positive integer. Find the maximum value of a3k−1b+b3k−1c+c3k−1a+k2akbkck,a^{3k-1}b+b^{3k-1}c+c^{3k-1}a+k^2a^kb^kc^k, where aa, bb, cc are non-negative reals such that a+b+c=3ka+b+c=3k.
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