olymmath

US-TST 2009 Problem 9

    Prove that for positive real numbers xx , yy , zz , x3(y2+z2)2+y3(z2+x2)2+z3(x2+y2)2≥xyz[xy(x+y)2+yz(y+z)2+zx(z+x)2].x^3(y^2+z^2)^2 + y^3(z^2+x^2)^2+z^3(x^2+y^2)^2 \geq xyz\left[xy(x+y)^2 + yz(y+z)^2 + zx(z+x)^2\right]. Zarathustra (Zeb) Brady.

    Dataset text AI-MO AoPS. Quoted with source.

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