Question Number 204686 by Davidtim last updated on 25/Feb/24
$$\sqrt{{a}−\sqrt{{a}−\sqrt{{a}−\centerdot\centerdot\centerdot}}}=? \\ $$
Commented by A5T last updated on 25/Feb/24
$${If}\:\sqrt{{a}−\sqrt{{a}−\sqrt{{a}−...}}}\:{converges},\:{then}\:\sqrt{{a}−{x}}={x} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +{x}−{a}=\mathrm{0}\Rightarrow{x}=\frac{−\mathrm{1}\underset{−} {+}\sqrt{\mathrm{1}+\mathrm{4}{a}}}{\mathrm{2}} \\ $$