+0  
 
-1
94
1
avatar+902 

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

 Sep 9, 2018
 #1
avatar+3621 
+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

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.