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Minimum value of function

Source: 2005 China Second Round Olympiad

September 2, 2014
functioninequalities unsolvedinequalitiesChinaalgebrainequalities proposedInequality

Problem Statement

Assume that positive numbers a,b,c,x,y,za, b, c, x, y, z satisfy cy+bz=acy + bz = a, az+cx=baz + cx = b, and bx+ay=cbx + ay = c. Find the minimum value of the function f(x,y,z)=x2x+1+y2y+1+z2z+1. f(x, y, z) = \frac{x^2}{x+1} + \frac {y^2}{y+1} + \frac{z^2}{z+1}.
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