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27 June, 18:10

Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)

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  1. 27 June, 18:27
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    4 and 4

    Step-by-step explanation:

    We have 2 numbers that will be X and Y

    X * Y = 16 = > Y = 16 / X

    We must minimize the sum, therefore:

    S = X + Y

    S = X + 16 / X

    we derive and equal 0 and we are left with:

    dS / dA = 1 - 16 / (X ^ 2) = 0

    1 = 16 / X ^ 2

    X ^ 2 = 16

    X = 4

    in the case of Y:

    Y = 16/4 = 4

    Therefore the numbers are 4 and 4.
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