Calculus

find the two numbers whose sum of the squares is a minimum if the product of the numbers is 10.

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  1. xy = 10, so y=10/x

    z = x^2+y^2 = x^2 + 100/x^2
    dz/dx = 2x - 200/x^3
    = (2x^2-200)/x^3

    dz/dx=0 when x=±10

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  2. find two numbers whose product is 16 and whose sum of squares is minimum.

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