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Find the value of \(6+\frac{1}{2+\frac{1}{6+\frac{1}{2+\frac{1}{6+\cdots}}}}\). Your answer should be in the form of \(a+b\sqrt{c}\) where no factor of c (other than 1) is a square. Find a+b+c

 Aug 3, 2020
 #1
avatar+31296 
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Like so:

 

I'll leave you to solve the quadratic equation.

 Aug 3, 2020
 #2
avatar+461 
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That helped a lot! Thanks . But wouldn't a quadratic equation have two solutions?

 Aug 3, 2020
 #3
avatar+31296 
+1

Yes but would they both be a valid solution to the original?  The original expression has to be positive.  Will that be true of the soutions to the quadratic?

Alan  Aug 3, 2020
 #4
avatar+461 
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Ohhh that makes so much more sense!

TYSM! :D

 Aug 3, 2020

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