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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.

 Jul 28, 2020
 #1
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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.

 Jul 28, 2020

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