Question Number 149268 by Samimsultani last updated on 04/Aug/21

Answered by dkenechukwu04 last updated on 04/Aug/21

Let 2+(3/(2+(3/(2+(3/(2+...))))))=x 5+(2/x)=5+(2/(2+(3/x))) 5+(2/x)=5+((2x)/(2x+3)) ((5x+2)/x)=((12x+15)/(2x+3)) 10x^2 +19x+6=12x^2 +15x 2x^2 −4x−6=0 x^2 −2x−3=0 (x−3)(x+1)=0 ∴x=3; x=-1 when x=3 5+(2/x)=5+(2/3) =5.67 when x=-1 5+(2/x)=5+(2/(-1)) =3

Answered by nimnim last updated on 04/Aug/21

Let (3/(2+(3/(2+(3/(2+(3/._._. )))))))=x, then (3/(2+x))=x⇒x^2 +2x−3=0 ⇒ x=1 or −3 (neglected) So, our question becomes 5+(2/(2+1))=((17)/3)★

Answered by john_santu last updated on 04/Aug/21

let 2+(3/(2+(3/(2+(3/⋮))))) = x ⇒x = 2+(3/x) ; x^2 −2x−3=0 ⇒(x−3)(x+1)=0 ⇒x = 3 or x=−1(rejected) then 5 +(2/x) = 5+(2/3)=((17)/3)

Answered by Ar Brandon last updated on 04/Aug/21

S=(3/(2+(3/(2+(3/(2+(3/⋱))))))), S>0 ⇒S=(3/(2+S))⇒S^2 +2S−3=0 ⇒(S+3)(S−1)=0⇒S=1, S=−3 ⇒5+(2/(2+(3/(2+(3/(2+(3/(2+(3/⋱)))))))))=5+(2/(2+S))=5+(2/3)=((17)/3)