Radicals and Quartic Equations

Algebra Level 4

If the solution of the equation x44x16=2x\sqrt { { x }^{ 4 }-4x-16 } =2-x can be written as x=abx=a\sqrt { b } such that aa and bb are coprimes, then the correct value of a+ba+b is __________\text{\_\_\_\_\_\_\_\_\_\_} .


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