# Joel's Problem 3: All good... with exceptions

Algebra Level 5

Consider the infinite sequence of real numbers $$x_{1}, x_{2}, x_{3}$$ ... such that for all positive integers $$n$$, $x_{n+1}=\frac {(2-\sqrt{3})+x_{n}}{1-(2-\sqrt {3})x_{n}}.$

For some values of $$x_{1}$$, there would exist a term of the sequence that is undefined. How many such values are there?

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