# Christian's maximum and minimum

Algebra Level 5

Let $$x$$ and $$y$$ be real numbers satisfying $$4x^2 + 5y^2 = 1$$. Over all such pairs, let the maximum and minimum values of $$2x^2 + 3xy + 2y^2$$ be $$M$$ and $$N$$ respectively. If $$M+N + MN = \frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b$$?

This problem is posed by Christian L.

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