Question Number 160832 by cortano last updated on 07/Dec/21
$$\:\sqrt{\mathrm{2021}−\mathrm{2}\sqrt{\mathrm{2021}−\mathrm{2}\sqrt{\mathrm{2021}−\mathrm{2x}}}}\:=\:\mathrm{x} \\ $$$$\:\mathrm{x}=? \\ $$
Answered by Raxreedoroid last updated on 07/Dec/21
$${x}=\sqrt{\mathrm{2021}−\mathrm{2}{x}} \\ $$$${x}^{\mathrm{2}} =\mathrm{2021}−\mathrm{2}{x} \\ $$$${x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2021}=\mathrm{0} \\ $$$${x}=−\mathrm{1}\pm\sqrt{\mathrm{2022}} \\ $$
Commented by mr W last updated on 07/Dec/21
$${x}=\sqrt{....}\:>\mathrm{0} \\ $$$$\Rightarrow{only}\:{x}=−\mathrm{1}+\sqrt{\mathrm{2022}}\:{is}\:{root}. \\ $$