Try this.
Now, perform the iterations.
Hopefully, it convegres to the solutions. It may not do it too fast, though.
(I made a pathetic mistake instead of it should be for ).
Consider the positive solution is .
Now it means
You form the continued fraction or simply 1's so .
Now let represent the fraction (approximation) after the terms.
So and the difference between the real value is .
Now and the difference between the real value is .
This tells us the difference between the approximation and the actual value gets very close.