Problem

Source: China TST 1988, problem 1

Tags: inequalities, quadratics, inequalities unsolved



Suppose real numbers A,B,C such that for all real numbers x,y,z the following inequality holds: A(xy)(xz)+B(yz)(yx)+C(zx)(zy)0. Find the necessary and sufficient condition A,B,C must satisfy (expressed by means of an equality or an inequality).