Question Number 88881 by Power last updated on 13/Apr/20
Answered by mahdi last updated on 13/Apr/20
$$\mathrm{A}=\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−…}}}}}} \\ $$$$\mathrm{A}=\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−\mathrm{A}}}}\Rightarrow\mathrm{A}^{\mathrm{2}} =\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}−\mathrm{A}}} \\ $$$$\mathrm{A}\backsimeq\mathrm{2}.\mathrm{5070} \\ $$