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x-1-x-x-2-1-x-x-1-




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

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