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Question Number 188704 by mathlove last updated on 05/Mar/23

Answered by a.lgnaoui last updated on 05/Mar/23

$$posonsZ=avec:A=x\sqrt{x}-x=x(\sqrt{x}-1)$$$$B=\frac{\sqrt[4]{x^3}-1}{\sqrt[4]{x}-1}-\sqrt{x}C=\frac{\sqrt[4]{x^3}+1}{\sqrt[4]{x}+1}-\sqrt{x}$$$$B=\frac{\sqrt{x}-1}{\sqrt[4]{x}-1}C=\frac{1-\sqrt{x}}{\sqrt[4]{x}+1}B\times C=1-\sqrt{x}$$$$\Rightarrow \frac{A}{B\times C}=\frac{x(\sqrt{x}-1)}{\sqrt{x}-1}$$$$Z^3={\left(\frac{\mathit{x}\sqrt{\mathit{x}}-1}{1-\sqrt{\mathit{x}}}\right)}^3=$$$$$$$${\left[\frac{\mathit{x}\sqrt{\mathit{x}}-\mathit{x}}{(\frac{\sqrt[4]{{\mathit{x}}^3}-1}{\sqrt[4]{\mathit{x}}-1}-\sqrt{\mathit{x}})(\frac{\sqrt[4]{{\mathit{x}}^3}+1}{\sqrt[4]{\mathit{x}}+1}-\sqrt{\mathit{x}})}\right]}^3=-{\mathit{x}}^3.$$

Commented by mathlove last updated on 06/Mar/23

$$thanks$$

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