Write \(x = {1+\frac{\sqrt{2}}{1+\frac{\sqrt{2}}{1+...}}}\) in the form \(x = \frac{A+B\sqrt{C}}{D}\),where A, B, C, and D are integers with greatest common divisor of 1.
Step 1) Write as: x = 1 + sqrt(2) / x
Step 2) Multiply each term by x.
Step 3) Gather all terms on one side.
Step 4) Use the quadratic formula.
