olymmath

JBMO-SL 2018 A1

    Let x,yx, y and zz be positive numbers. Prove that

    xy4+z4+yz4+x4+zx4+y4≥(x+y+z)74227\frac{x}{\sqrt{\sqrt[4]{y}+\sqrt[4]{z}}}+\frac{y}{\sqrt{\sqrt[4]{z}+\sqrt[4]{x}}}+\frac{z}{\sqrt{\sqrt[4]{x}+\sqrt[4]{y}}} \geq \frac{\sqrt[4]{(\sqrt{x}+\sqrt{y}+\sqrt{z})^{7}}}{\sqrt{2 \sqrt{27}}}

    Dataset text NuminaMath olympiads. Quoted with source.

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