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Given that $$x = {1+\frac{\sqrt{2}}{1+\frac{\sqrt{2}}{1+...}}}$$, 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|?

May 30, 2021

$\frac{1}{(x + 1)(x - 2)} = \frac{-7 - \sqrt{2}}{5}$, so $|A| + |B| + |C| = 14$.