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P(x) + P(y) + P(z) > 0

Source: Bulgarian National Olympiad 2012 Problem 5

May 21, 2012
quadraticsfunctionalgebra proposedalgebra

Problem Statement

Let Q(x)Q(x) be a quadratic trinomial. Given that the function P(x)=x2Q(x)P(x)=x^{2}Q(x) is increasing in the interval (0,āˆž)(0,\infty ), prove that: P(x)+P(y)+P(z)>0P(x) + P(y) + P(z) > 0 for all real numbers x,y,zx,y,z such that x+y+z>0x+y+z>0 and xyz>0xyz>0.
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