x-3-xyz-1-y-3-xyz-2-z-3-xyz-3-

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

{\begin{cases} x^{3} = xyz + 1 \\ y^{3} = xyz + 2 \\ z^{3} = xyz - 3 \end{cases}

Commented by bramlexs22 last updated on 14/May/21

Thank all master

Answered by EDWIN88 last updated on 14/May/21

(1) \times (2) \times (3) . let ℓ = xyz

\Rightarrow ℓ^{3} = (ℓ + 1) (ℓ + 2) (ℓ - 3)

\Rightarrow ℓ = - \frac{6}{7} = xyz

\Rightarrow x^{3} = \frac{1}{7} \Rightarrow x = \frac{1}{\sqrt[3]{7}}

\Rightarrow y^{3} = \frac{8}{7} \Rightarrow y = \frac{2}{\sqrt[3]{7}}

\Rightarrow z^{3} = - \frac{27}{7} \Rightarrow z = - \frac{3}{\sqrt[3]{7}}

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