Question Number 188981 by Mingma last updated on 10/Mar/23
Answered by HeferH last updated on 10/Mar/23
Commented by HeferH last updated on 13/Mar/23
$$\:\frac{{r}+\mathrm{1}}{\:\sqrt{\mathrm{5}}+\mathrm{1}}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}} \\ $$$$\:{r}\:=\:\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}\:−\:\mathrm{1}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{5}}+\mathrm{2}}{\mathrm{4}}\:=\:\frac{\mathrm{1}\:+\sqrt{\mathrm{5}}}{\mathrm{2}}\: \\ $$