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Inequality

Source: Silk Road Mathematival Competition , P3

May 25, 2017
inequalities proposedinequalitiessrmc

Problem Statement

Prove that among any 4242 numbers from the interval [1,106][1,10^6], you can choose four numbers so that for any permutation (a,b,c,d)(a, b, c, d) of these numbers, the inequality 25(ab+cd)(ad+bc)≥16(ac+bd)225 (ab + cd) (ad + bc) \ge 16 (ac + bd)^ 2 holds.
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