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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