We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
-1
211
1
avatar+1206 

Evaluate \(\sqrt{12 +\!\sqrt{12 + \!\sqrt{12 + \!\sqrt{12 + \cdots}}}}\).

 Sep 9, 2018
 #1
avatar+5652 
+1

let that expression equal x, then

 

\(\sqrt{12+x}=x \\ 12 + x = x^2 \\ x^2 -x -12 = 0 \\ (x-4)(x+3) = 0 \\ x = 4,~-3 \\ \text{however as x is a square root x > 0, thus }x=4\)

.
 Sep 9, 2018

12 Online Users