Posted by Mark on .
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?

Math (algebra) 
Steve,
M = .789116
N = .110884
MN = .087500
M+N+MN = .987500 = 79/80