Hey Suvadip.
Is it possible to use the Hessian for this system?
It seems to me the simplest way is just to graph it. Using x= x1, y= x2, the graph of y^2= 4x is a parabola and the set {(x, y)| y^2>= x} is the set of points outside the parabola. That would lead me to look at the points (1, 2) and (1, -2). 2^2= 4> 1 and (-2)^2> 1 so both (1, 2) and (1, -2) is in the set. But (1, 0) is NOT.