The Root Of All Roots

Algebra Level 4

If the roots of the equation

$\sqrt {x^2 + {\sqrt { x^2+11}}} + \sqrt {x^2 - {\sqrt {x^2+11}}} = 4$

are of the form $$a \pm \sqrt{b}$$, where $$a$$ and $$b$$ are integers, find the value of $$a^2 + 3ab +b^2$$.

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