olymmath

JBMO-SL 2009 A5

Let x,y,zx, y, z be positive real numbers. Prove that:

(x2+y+1)(x2+z+1)(y2+z+1)(y2+x+1)(z2+x+1)(z2+y+1)≥(x+y+z)6\left(x^{2}+y+1\right)\left(x^{2}+z+1\right)\left(y^{2}+z+1\right)\left(y^{2}+x+1\right)\left(z^{2}+x+1\right)\left(z^{2}+y+1\right) \geq(x+y+z)^{6}

Dataset text NuminaMath olympiads. Quoted with source.

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