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2 January, 08:13

Find the pair of numbers whose sum is 46 and whose product is a maximum.

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  1. 2 January, 08:45
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    To solve this problem you must apply the proccedure shown below:

    1. Let's call:

    x the first number and and the other number 46-x

    2. Then, the product of both numbers is:

    y=x (46-x)

    3. When you apply the distributive property, you obtain:

    y=46x-x^2

    4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.

    5. Then, you have:

    h=-b/2a

    h=-46/2 (-1)

    h=23 (x coordinate)

    6. Then:

    y=46x-x^2

    y=46 (23) - (23) ^2

    y=529

    Therefore the answer is: 23 and 529.
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