Find two positive numbers whose sum is 50 such that the sum of their squares is minimum?

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  1. let one number be x
    then the other is 50-x

    let the sum of their squares be S
    S = x^2 + (50-x)^2
    = 2x^2 - 100x + 2500
    dS/dx = 4x - 100
    = 0 for a min of S
    4x-100 = 0
    x = 25

    The numbers are 25 and 25

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