x(x-1)-(x^2-y)=-2
x^2-x-x^2+y=-2
-x+y=-2
x-y=2
(x^2+y^2)/2-2y+2x-xy
=(x^2-2xy+y^2)/2+(2x-2y)
=(x-y)^2/2+2(x-y)
=2^2/2+2*2
=2+4
=6