Question Number 218474 by Nicholas666 last updated on 10/Apr/25
$$ \\ $$$$\:\:\:\:{solve}\:{for}\:{real}\:\boldsymbol{{x}} \\ $$$$\:\:\:\:\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:=\:\sqrt{\mathrm{2}} \\ $$$$ \\ $$
Answered by mehdee7396 last updated on 10/Apr/25
$${x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}=\mathrm{2} \\ $$$${x}^{\mathrm{2}} +\mathrm{1}={x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}\Rightarrow{x}=\frac{\mathrm{3}}{\mathrm{4}}\:\checkmark \\ $$$$ \\ $$