If I use (sqrt(|x|) - 1/sqrt(|x|) )^2 and compare that with [- A +- sqrt(A^2 - 4(B-2))] / 2, I get something like B =< 2A -2.
But that doesn't seem right - then B =< -2, unless I've mixed up a sign somewhere.
Also, if x not real, then I'm not sure how that comparison works. Taking |x| would be...