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March 25, 2017

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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) - ,

    M = .789116
    N = .110884
    MN = .087500

    M+N+MN = .987500 = 79/80

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