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Question Number 127525 by Mathgreat last updated on 30/Dec/20

Commented by Mathgreat last updated on 30/Dec/20

$${\mathit{x}}_1+{\mathit{x}}_2+{\mathit{x}}_3+...+{\mathit{x}}_{\mathit{n}}=???$$

Commented by Mathgreat last updated on 30/Dec/20

$$\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}$$

Answered by MJS_new last updated on 31/Dec/20

$$x^{7/3}=x^n$$$$n\in \mathbb{N}(?)$$$$n=0\Rightarrow x^{7/3}=1\Rightarrow x=1$$$$n⩾1$$$$\left(1\right)\mathrm{if}\mathrm{we}\mathrm{stay}\mathrm{in}\mathbb{R}\Rightarrow \sqrt[3]{-x}=-\sqrt[3]{x}$$$$\Rightarrow \{\begin{array}{l}n=2k;x=0\vee x=1\\ n=2k+1;x=-1\vee x=0\vee x=1\end{array}$$$$\left(2\right)\mathrm{if}{\mathrm{we}}^{\prime }\mathrm{re}\mathrm{in}\mathbb{C}\Rightarrow \sqrt[3]{-x}=\sqrt[3]{\mathrm{abs}\left(x\right)}{\mathrm{e}}^{\mathrm{i}\arg \left(x\right)/3}$$$$\Rightarrow x=0\vee x=1$$

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