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16 August, 07:21

What two positive real numbers whose product is 50 have the smallest possible sum?

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  1. 16 August, 07:51
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    X * y = 50

    y = 50 / x

    S = x + y = x + 50 / x

    S' = 1 - 50 / x²

    1 - 50 / x² = 0

    50 / x² = 1

    x² = 50

    x = √ 50 = 5 √2

    y = 50 / 5√2 = 5 √2

    Answer:

    Those numbers are: x = 5√2 and y = 5√2.
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