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Question:

alquigg
alquigg
Student
High School - 11th Grade

Find the minimum product of two numbers whose difference is nine.

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Posted by alquigg on Friday February 20, 2009 at 4:02 PM and tagged with completing the square, math.

Answers:

  1. cburr
    cburr Teacher
    Middle School

    eNotes Editor

    Assuming we aren't dealing with negative or fractional numbers, the smallest product would have to be 0. The numbers 9 and 0 have a difference of 9 and when multiplied together the product is 0.

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    Posted by cburr on Friday February 20, 2009 at 4:10 PM


  2. santari

    eNotes Editor

    If you are not limited to positive numbers or integers, you would be locating the vertex of the parabola using the parabolic equation:

    y = ax^2 + bx + c

    In this case we have:
    y = x(x+9)
    y = x^2 + 9x

    The x coordinate of the vertex is found by using the equation:

    -b/2a

    In this case b is 9 and a is 1, so

    -9/2 = -4.5

    The minimum value will be when x = -4.5 and x + 9 = 4.5, so:

    -4.5*4.5 = -20.25

    -20.25 is the minimum product.

    Sources:
    http://a-s.clayton.edu/garrison/Math%200099/parabola.htm

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    Posted by santari on Friday February 20, 2009 at 6:19 PM