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Maximum value of x_i*x_j* (x_i + x_j) summed over all i

Source: IMO ShortList 1991, Problem 27 (POL 2)

August 15, 2008

inequalitiesIMO Shortlistmaximum valuemaximization

Problem Statement

Determine the maximum value of the sum \sum_{i < j} x_ix_j (x_i \plus{} x_j) over all n \minus{}tuples

(x_1, \ldots, x_n),

satisfying

x_i \geq 0

and \sum^n_{i \equal{} 1} x_i \equal{} 1.