olymmath

RU-ALLRUSSIAN 1991 Problem 9

    Show that (x+y+z)2/3≥x(yz)+y(zx)+z(xy)(\mathrm{x} + \mathrm{y} + \mathrm{z})^{2} / 3 \geq \mathrm{x}\sqrt{(\mathrm{y}\mathrm{z})} + \mathrm{y}\sqrt{(\mathrm{z}\mathrm{x})} + \mathrm{z}\sqrt{(\mathrm{x}\mathrm{y})} for all non- negative reals x,y,z\mathrm{x}, \mathrm{y}, \mathrm{z} .

    Dataset text NuminaMath olympiads. Quoted with source.

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