Minimum value too dangerous

Algebra Level 4

433x2+y2+1729xy+3x3y+1729!433x^{2}+y^{2}+\sqrt{1729}xy+\sqrt{3}x-\sqrt{3}y+1729!

For real values of xx and yy the above expression attains minimum value at x=Mx=M and y=Ny=N. And M+N=abM+N=a\sqrt{b}, where aa is positive integer and bb is square-free. Find aba-b.

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