if-x-y-z-gt-0-and-xyz-1-prove-that-x-4-x-yz-y-4-y-zx-z-4-z-xy-3-2-

Question Number 149212 by mathdanisur last updated on 03/Aug/21

$${if}\:\:\:{x};{y};{z}>\mathrm{0}\:\:\:{and}\:\:\:{xyz}=\mathrm{1}\:\:\:{prove}\:{that}: \\ $$$$\frac{{x}^{\mathrm{4}} }{{x}+{yz}}\:+\:\frac{{y}^{\mathrm{4}} }{{y}+{zx}}\:+\:\frac{{z}^{\mathrm{4}} }{{z}+{xy}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$

Answered by dumitrel last updated on 03/Aug/21

Commented by mathdanisur last updated on 03/Aug/21

$${Ser},\:{Thank}\:{You} \\ $$

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