Question Number 135108 by bramlexs22 last updated on 10/Mar/21
$$\left(\sqrt{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}}\:\right)^{\mathrm{x}^{\mathrm{2}} } \:=\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} \\ $$
Answered by MJS_new last updated on 10/Mar/21
$${x}^{\mathrm{2}} ={x}+\mathrm{1}\:\Leftrightarrow\:\frac{{x}−\mathrm{1}}{{x}}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$$\Rightarrow \\ $$$${x}=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$