# Minimum value too dangerous

Algebra Level 5

$433x^{2}+y^{2}+\sqrt{1729}xy+\sqrt{3}x-\sqrt{3}y+1729!$ For real values of $$x,y$$ the above expression attains minimum value at $$x=M,y=N$$ . And $$M+N=a\sqrt{b}$$ where $$a$$ is positive integer and $$b$$ is square root free. Find $$a-b$$.

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