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

if   x;y;z>0   and   xyz=1   prove that:  (x^4 /(x+yz)) + (y^4 /(y+zx)) + (z^4 /(z+xy)) ≥ (3/2)

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

Answered by dumitrel last updated on 03/Aug/21

Commented by mathdanisur last updated on 03/Aug/21

Ser, Thank You

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

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