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Let xxx and yyy be real numbers satisfying 4x2+5y2=14x^2 + 5y^2 = 14x2+5y2=1. Over all such pairs, let the maximum and minimum values of 2x2+3xy+2y22x^2 + 3xy + 2y^22x2+3xy+2y2 be MMM and NNN respectively. If M+N+MN=abM+N + MN = \frac{a}{b}M+N+MN=ba, where aaa and bbb are coprime positive integers, what is the value of a+ba+ba+b?
This problem is posed by Christian L.
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