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A(x-y)(x-z) + B(y-z)(y-x) + C(z-x)(z-y) >= 0

Source: China TST 1988, problem 1

June 27, 2005
inequalitiesquadraticsinequalities unsolved

Problem Statement

Suppose real numbers A,B,CA,B,C such that for all real numbers x,y,zx,y,z the following inequality holds: A(x−y)(x−z)+B(y−z)(y−x)+C(z−x)(z−y)≥0.A(x-y)(x-z) + B(y-z)(y-x) + C(z-x)(z-y) \geq 0. Find the necessary and sufficient condition A,B,CA,B,C must satisfy (expressed by means of an equality or an inequality).
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