# Thread: Solve for X - square root infinite

1. ## Solve for X - square root infinite

Solve for x:

x = $\sqrt{3+\sqrt{3+\sqrt{3+...}}}$

I have been stuck on this problem, was hoping for some help. Really confused about the square root under the square root and so on to infinity. Not sure where to begin hoping to be showed steps that get me to an answer. Thanks

2. Originally Posted by kelly1183
Solve for x:

x = $\sqrt{3+\sqrt{3+\sqrt{3+...}}}$

I have been stuck on this problem, was hoping for some help. Really confused about the square root under the square root and so on to infinity. Not sure where to begin hoping to be showed steps that get me to an answer. Thanks
Hi

You can see that

$x^2 = 3+\sqrt{3+\sqrt{3+...}}$

$x^2 - 3 = \sqrt{3+\sqrt{3+...}}$

$x^2 - 3 = x$

This is a quadratic which has only one positive root