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Question Number 107234 by O Predador last updated on 09/Aug/20

Answered by floor(10²Eta[1]) last updated on 09/Aug/20

$${\mathrm{x}}^{\frac{1}{\sqrt{7}}}+\frac{7}{{\mathrm{x}}^{\frac{\sqrt{7}}{7}}}=8$$$$\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}$$$${\mathrm{x}}^{\frac{1}{\sqrt{7}}}=\mathrm{y}\Rightarrow \mathrm{y}+\frac{7}{\mathrm{y}}=8\Rightarrow {\mathrm{y}}^2-8\mathrm{y}+7=0$$$$\mathrm{y}=\frac{8\pm 6}{2}=7,1={\mathrm{x}}^{\frac{1}{\sqrt{7}}}$$$$\Rightarrow \mathrm{x}=7^{\sqrt{7}}\mathrm{ou}\mathrm{x}=1$$

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