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Question Number 153381 by mathdanisur last updated on 06/Sep/21

$$\mathrm{let}\mathrm{x};\mathrm{y};\mathrm{z}⩾0\mathrm{and}{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=12$$$$\mathrm{find}\mathrm{the}\min \mathrm{value}\mathrm{of}$$$$\mathrm{S}=\mathrm{x}+\mathrm{y}+\mathrm{z}+\mathrm{xyz}+\frac{1}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$$

Commented by mr W last updated on 06/Sep/21

$$S_{min}=3\times 2+2^3+\frac{1}{3\times 2^2}=\frac{169}{12}$$

Commented by mathdanisur last updated on 07/Sep/21

$$\mathrm{No}\mathrm{ser}=\frac{9}{2}$$

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