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Word problem solved by applying a quadratic equation

  1. Aug 9, 2007 #1
    This is a simple word problem that I just can't wrap my head around. The answers are 7 and 9:

    The sum of two numbers is 16, but the sum of their squares is 130. Find the numbers.

    I am supposed to use a quadratic equation as a means to solve the question, and all I need to do is to create an equation to get started. Thing is, I've got no idea what to use. Well I had one but it was horribly wrong.

    Here's how I reached the wrong answer:
    2n^2 + 2n = 130 + 16
    2n^2 + 2n - 146 = 0

    Then I just used the quadratic formula to find the set of numbers which were wayy off. I'm sure the equation simply isn't right but I don't know how to set up the right one. This is where I get frustrated, because it seems like the answer should be jumping out at me.. but it's not.

    If anyone knows of an easy way to tackle these type of problems I would greatly appreciate the help.
    Last edited: Aug 10, 2007
  2. jcsd
  3. Aug 9, 2007 #2
    sum means a+b
    and, sum of squares = a^2+b^2

    if you can't solve this by quadratic, try substitution method instead
  4. Aug 9, 2007 #3


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    errr... how is 7^2+9^2 = 130 =? 440?
    check wording of problem
  5. Aug 9, 2007 #4
    [tex]x+y = 16[/tex]
    [tex]x^2+y^2 = 130[/tex]

    Just solve the system of equations
    Last edited: Aug 10, 2007
  6. Aug 10, 2007 #5
    I appreciate your feedback and solving the system of equations is a great suggestion, but I really need to do this question by using a quadratic equation.
    Oh and thanks for pointing out that mistake in the question, the sum of their sqaures actually equals 130 - I grabbed the number off the wrong question in my text.

    Does anyone know what equations I would use to end up having to solve this thing by factoring a quadratic equation?
  7. Aug 10, 2007 #6


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    Solve the two equations Feldoh posted
    x + y = 16

    When you try to solve this you will end up with a quadratic equation...
  8. Aug 10, 2007 #7


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    Use Feldoh's equations (with the corrected value of 130 instead of 440).
    Use elimination...
    ...say, solve the first equation for y, then use that expression in the second equation.
    ...alternatively, use the second equation in the square of the first equation.
  9. Aug 10, 2007 #8
    Sorry... Not really sure where 440 came from >.>
  10. Aug 10, 2007 #9
    Ooooh!!! I see now! See I haven't taken math in years so any question that relies on previously learned techniques tends to slip right by me, its pretty sad I have to go online and relearn things I was probably taught in middle school... haha oh well.. you guys are all a huge help! Thank you for pointing out the glaringly obvious! :!!)

    And thank you robphy and feldoh!
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