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Question Number 93039 by i jagooll last updated on 10/May/20

$$\{\begin{array}{l}xy+yz=8\\ yz+xz=9\\ zx+xy=5\end{array}$$

Commented by i jagooll last updated on 10/May/20

$$2\mathrm{xy}+2\mathrm{xz}+2\mathrm{yz}=22$$$$\mathrm{xy}+\mathrm{xz}+\mathrm{yz}=11$$$$\Rightarrow \mathrm{xz}=3,\mathrm{yz}=6,\mathrm{xy}=2$$$${\left(\mathrm{xyz}\right)}^2=36\Rightarrow \mathrm{xyz}=\pm 6$$$$\left(1\right)\mathrm{xyz}=6\{\begin{array}{l}\mathrm{x}=1\\ \mathrm{y}=2\\ \mathrm{z}=3\end{array}$$$$\left(2\right)\mathrm{xyz}=-6\{\begin{array}{l}\mathrm{x}=-1\\ \mathrm{y}=-2\\ \mathrm{z}=-3\end{array}$$

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