# Solve for X - square root infinite

• May 4th 2010, 10:49 AM
kelly1183
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
• May 4th 2010, 10:58 AM
running-gag
Quote:

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