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Minimum of cyclic Σ ( x^2 + x/(y^2+z+1) )

Source: Czech-Polish-Slovak Match, 2010

August 8, 2011
inequalitiesinequalities unsolved

Problem Statement

Let xx, yy, zz be positive real numbers satisfying x+y+z≥6x+y+z\ge 6. Find, with proof, the minimum value of x2+y2+z2+xy2+z+1+yz2+x+1+zx2+y+1. x^2+y^2+z^2+\frac{x}{y^2+z+1}+\frac{y}{z^2+x+1}+\frac{z}{x^2+y+1}.
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