Why Ask Why (YXY)

For $x$ and $y$ satisfying $\displaystyle \sqrt{x^2 - 20 \sqrt{6}} = \displaystyle \sqrt{20 \sqrt{6} - y} = 7$ there is a minimal polynomial of integer coefficients such that $A = x + y^2$ is a root. If the other root if $B$ , evaluate the digit sum of $801\left (\dfrac{AB}{A + B} + \dfrac{A + B}{AB} \right )$ .