could produce an extra false solution. Your example (2+(2+...)^.5)^.5 is the one. We will get x=(2+x)^.5. We get x^2=2+x. We need to discard -1 as the solution. The reason is the same. So there is no mistry about original problem.
It is interesting to know that (2^.5)^(2^.5)^...= (2+(2+...)^.5)^.5.
