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inequality for real numbers and 2 sums

Source: Problem 3, Polish NO 1992

October 1, 2005
inequalitiesfunction

Problem Statement

Show that for real numbers x1,x2,...,xnx_1, x_2, ... , x_n we have: ∑i=1n∑j=1nxixji+j≥0 \sum\limits_{i=1}^n \sum\limits_{j=1}^n \dfrac{x_ix_j}{i+j} \geq 0 When do we have equality?
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