Question Number 173028 by mnjuly1970 last updated on 05/Jul/22
Answered by MJS_new last updated on 05/Jul/22
$${x}=\mathrm{0} \\ $$
Answered by MJS_new last updated on 05/Jul/22
$${x}=\mathrm{0}\vee{x}\geqslant\mathrm{1}\:\left(\mathrm{because}\:{x}−\sqrt{{x}}\geqslant\mathrm{0}\right) \\ $$$$\mathrm{if}\:{x}−\sqrt{{x}}=\mathrm{1}\:\Leftrightarrow\:\sqrt{{x}}={x}−\mathrm{1} \\ $$$${x}\left({x}−\mathrm{1}\right)+\mathrm{1}=\mathrm{2}{x} \\ $$$${x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\:{x}=\frac{\mathrm{3}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$