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