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turkey nmo 2006 q4

Source:

January 6, 2007

inequalities unsolvedinequalities

Problem Statement

x_{1},...,x_{n}

are positive reals such that their sum and their squares' sum are equal to

t

. Prove that

\sum_{i\neq{j}}\frac{x_{i}}{x_{j}}\ge\frac{(n-1)^{2}\cdot{t}}{t-1}