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Let \(x = {1+\frac{\sqrt{2}}{1+\frac{\sqrt{2}}{1+ \dotsb}}}.\)

 

 

Find \(\frac{1}{(x+1)(x-2)}\). When your answer is in the form \(\frac{A+\sqrt{B}}{C}\) , where A , B , and C are integers, and B is not divisible by the square of a prime, what is \(|A|+|B|+|C|\)?

 
 Aug 5, 2022
 #2
avatar+117737 
+1

 

This is just

 

\(x=1+\frac{\sqrt2}{x}\)

 

 

Now take it from there.

 

If you need to interact further then feel free to do so.

 
 Aug 7, 2022

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