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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