# Calculate the quadratic irrational number given by a certain periodic cont. fraction

Calculate the quadratic irrational number $\alpha$ given by the periodic continued fraction $\alpha = \overline{ [1,2,1] }$.

To be honest I am not sure how to tackle this one. I know the algorithm to construct a continued fraction given $\alpha$, but I am unsure how to reverse this algorithm.

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$\alpha = 1+\cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{\alpha }}}$