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Question Number 135108 by bramlexs22 last updated on 10/Mar/21

$${\left(\sqrt{\frac{\mathrm{x}-1}{\mathrm{x}}}\right)}^{{\mathrm{x}}^2}={\left(\frac{1}{\mathrm{x}}\right)}^{\mathrm{x}+1}$$

Answered by MJS_new last updated on 10/Mar/21

$$x^2=x+1\iff \frac{x-1}{x}=\frac{1}{x^2}$$$$\Rightarrow$$$$x=\frac{1+\sqrt{5}}{2}$$

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