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Question Number 140900 by bramlexs22 last updated on 14/May/21

$$\{\begin{array}{l}{\mathrm{x}}^3=\mathrm{xyz}+1\\ {\mathrm{y}}^3=\mathrm{xyz}+2\\ {\mathrm{z}}^3=\mathrm{xyz}-3\end{array}$$

Commented by bramlexs22 last updated on 14/May/21

$$\mathrm{Thank}\mathrm{all}\mathrm{master}$$

Answered by EDWIN88 last updated on 14/May/21

$$\left(1\right)\times \left(2\right)\times \left(3\right).\mathrm{let}\ell =\mathrm{xyz}$$$$\Rightarrow {\ell }^3=(\ell +1)(\ell +2)(\ell -3)$$$$\Rightarrow \ell =-\frac{6}{7}=\mathrm{xyz}$$$$\Rightarrow {\mathrm{x}}^3=\frac{1}{7}\Rightarrow \mathrm{x}=\frac{1}{\sqrt[3]{7}}$$$$\Rightarrow {\mathrm{y}}^3=\frac{8}{7}\Rightarrow \mathrm{y}=\frac{2}{\sqrt[3]{7}}$$$$\Rightarrow {\mathrm{z}}^3=-\frac{27}{7}\Rightarrow \mathrm{z}=-\frac{3}{\sqrt[3]{7}}$$

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