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Calculate $\sqrt{3 + \sqrt{3 + \sqrt{3 + \dotsb}}}$.

 Feb 24, 2021
 #1
avatar+939 
+1

Let the entire thing be equal to x. Then,

 

\(\sqrt{3 + x} = x\)

 

\(3 + x = x^2\)

 

Use the quadratic formula to solve for x.

 Feb 24, 2021
 #2
avatar+30674 
+1

let x = your entire question

 

x^2 = 3  + sqrt 3 sqrt......

 

then x ^2  - x   = 3

x^2 -x-3   = 0                      then as Penguin said...use quadratic formula to find x  ( the positive value)

 Feb 24, 2021

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