Posted by **Mark** on Monday, July 15, 2013 at 1:08pm.

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=a/b, where a and b are coprime positive integers, what is the value of a+b?

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