Question Number 160908 by naka3546 last updated on 10/Dec/21
$${x},{y},{z}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{value}\:\:{of}\:\:{this}\:\:{expression}\: \\ $$$$\:\:\:\:\:\:\frac{{xyz}}{\left(\mathrm{1}+\mathrm{3}{x}\right)\left({x}+\mathrm{8}{y}\right)\left({y}+\mathrm{9}{z}\right)\left(\mathrm{6}+{z}\right)}\:\: \\ $$$$ \\ $$
Commented by mr W last updated on 25/Dec/21
$${do}\:{you}\:{know}\:{the}\:{solution}? \\ $$$${i}\:{think}\:{there}\:{exists}\:{no}\:{minimum}\:{and} \\ $$$${no}\:{maximun},\:{since}\:{with}\:{x}={y}={z}\rightarrow\mathrm{0} \\ $$$${it}\:\rightarrow+\infty\:{and}\:{with}\:{x}={y}={z}\rightarrow\infty\:{it}\:\rightarrow\mathrm{0}. \\ $$