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What is the sum of all possible real values of x, such that there exists a real value y which satisfies the equation (x+y−40)^2+(x−y−18)^2=0?

  • math -

    since all squares are >= 0, both squared expressions must be zero. So you need

    x+y-40 = 0 and
    x-y-18 = 0

    2x-58 = 0
    x = 29
    y = 11

    Only one real value for x satisfies the equation

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