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find two numbers whose product is N^2 and whose sum is a minimum

  • math -

    let one number be x, then the other is n^2/x
    sum = x + n^2/x
    d(sum)/dx = 1 - n^2/x^2 = 0 for a minimum
    n^2/x^2 = 1
    n/x = ± 1

    x = N or x = -N

    e.g. If N^2 = 144
    then both numbers would be 12 (or
    both numbers would be -12)

    factors of 144
    = 12x12 ---- sum = 24
    = 4x36 ---- sum = 40
    = 8x18 --- sum = 26
    etc.

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