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Question Number 158424 by HongKing last updated on 04/Nov/21

Answered by ghimisi last updated on 04/Nov/21

$$x^3+y^3+z^3+3\sqrt[3]{x}+3\sqrt[3]{y}+3\sqrt[3]{z}\stackrel{am-gm}{⩾}12\sqrt[12]{4x^4{y}^4{z}^4}=12\Rightarrow$$$$x^3=y^3=z^3=\sqrt[3]{x}=\sqrt[3]{y=}\sqrt[3]{z}\Rightarrow x=y=z=1$$$$$$

Commented by HongKing last updated on 04/Nov/21

$$\mathrm{thank}\mathrm{you}\mathrm{my}\mathrm{dear}\mathbf{S}\mathrm{er}\mathrm{cool}$$

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