Why Ask Why (YXY)

Algebra Level pending

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 \[801\left (\dfrac{AB}{A + B} + \dfrac{A + B}{AB} \right )\].

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