Question Number 221151 by gregori last updated on 25/May/25
$$\:\frac{\sqrt{{x}^{\mathrm{2}} −{x}−\sqrt{{x}^{\mathrm{2}} −{x}−\sqrt{{x}^{\mathrm{2}} −{x}−\sqrt{…}}}}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} \:\sqrt{{x}\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} \:\sqrt{{x}…}}}}}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\:\Rightarrow\:\frac{\mathrm{2}}{{x}}\:=?\: \\ $$
Commented by Frix last updated on 25/May/25
$$\frac{{x}−\mathrm{1}}{{x}}=\frac{\mathrm{3}}{\mathrm{4}}\:\Rightarrow\:{x}=\mathrm{4}\:\Rightarrow\:\frac{\mathrm{2}}{{x}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$