Why do we conclude that answer or x should only be positive?
I am asking from the algebraic perspective if x= 1/(3+x) then id x is negative the expression still holds.

Because every individual term in the expression is positive (1+3/1+3/1+3/1+…). For x = 1/(3+x) there will probably be two solutions, one positive and one negative (it is a quadratic after all). But the expression given, consisting as it does entirely of positive quantities, cannot yield a negative result.

Nice method to solve it

sir how 2 approach for square root of 4+ square root of 4 -square root of 4 and so on till infinity..

Why do we conclude that answer or x should only be positive?

I am asking from the algebraic perspective if x= 1/(3+x) then id x is negative the expression still holds.

Because every individual term in the expression is positive (1+3/1+3/1+3/1+…). For x = 1/(3+x) there will probably be two solutions, one positive and one negative (it is a quadratic after all). But the expression given, consisting as it does entirely of positive quantities, cannot yield a negative result.

regards

J