+0

# i have no idea

0
106
1

Find $$x = \sqrt{ 3 + \sqrt{ 3 + \sqrt{ 3 + \sqrt{ \ldots } } } }$$

Jun 30, 2020

#1
+307
+1

This equals $$x=\sqrt{3+x}$$

Square both sides $$x^2=3+x$$.

Then factorize $$x^2-x-3=0$$.

Since this expression is clearly positive, x=$$\frac{1+\sqrt{13}}{2}$$

Jun 30, 2020