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

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?