Radicals and Quartic Equations

Algebra Level 4

If the solution of the equation \(\sqrt { { x }^{ 4 }-4x-16 } =2-x\) can be written as \(x=a\sqrt { b }\) such that \(a\) and \(b\) are coprimes, then the correct value of \(a+b\) is \(\text{__________} \).


Source: Adapted from 1985's Lomonosov Moscow State University physics course admission exam.
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