Menu Close

Question-188981




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
 ((r+1)/( (√5)+1)) = (1/( (√5)−1))   r = (((√5)+1)/( (√5)−1)) − 1 = (2/( (√5)−1)) = ((2(√5)+2)/4) = ((1 +(√5))/2)
$$\:\frac{{r}+\mathrm{1}}{\:\sqrt{\mathrm{5}}+\mathrm{1}}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}} \\ $$$$\:{r}\:=\:\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}\:−\:\mathrm{1}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{5}}+\mathrm{2}}{\mathrm{4}}\:=\:\frac{\mathrm{1}\:+\sqrt{\mathrm{5}}}{\mathrm{2}}\: \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *