Radicals and Quartic Equations

Algebra Level 5

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 $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Radicals and Quartic Equations

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