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4 July, 13:28

Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.

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  1. 4 July, 17:14
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    Let the two required numbers be x and 100 - x, then

    Sum of its squares is given by S = x^2 + (100 - x) ^2

    For the sum of the squares to be minimum, dS/dx = 0

    dS/dx = 2x - 2 (100 - x) = 0

    2x - 200 + 2x = 0

    4x = 200

    x = 50.

    The two numbers is 50 and 50.
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