Question Number 114796 by Algoritm last updated on 21/Sep/20

Answered by MJS_new last updated on 21/Sep/20

y=(x/(2+y))=(x/(2+(x/(2+y))))=(x/(2+(x/(2+(x/(2+y))))))=...  ⇒ y=−1+(√(x+1))  but the last term 1+(√(x+1))=2+y  ⇒ solution is −1+(√(x+1))

Answered by PRITHWISH SEN 2 last updated on 21/Sep/20

the last term = 2+(x/(1+(√(x+1)))) = ((x+2+2(√(x+1)))/(1+(√(x+1))))       = ((((√(x+1))+1)^2 )/(((√(x+1))+1)) = (√(x+1)) +1  and the previous to the last term is      = 2+(x/(1+(√(1+x)))) = last term  ∴ the expression becomes = (x/( (√(x+1))+1)) = (√(x+1))−1