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Math Help - Finding unknown variables

  1. #1
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    Finding unknown variables

    Two numbers are each multiplied by themselves to give two new numbers. The difference between these two new numbers is less than ten; the difference between the two original numbers was one.
    The two original numbers added together was more than 7. What is one of the original numbers?



    Let x and y represent the first two numbers


    Let a and b represent the two new numbers


    xy=ab


    a-b < 10


    x-y = 1


    x + y > 7


    Am i on the right path?


    What do I do next?
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Finding unknown variables

    I think the first sentence means that you have two numbers, say x and y, and they are each squared... this gives you x^2 and y^2 (two "new numbers").

    Then x^2 - y^2 < 10
    x - y = 1
    x + y > 7
    Multiply the last two together to get
    x^2 - y^2 = (x + y)(x - y) > 7 * 1 = 7
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  3. #3
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    Re: Finding unknown variables

    I'm still at a loss.I don't quite get it.

    Anyone has further leads?
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  4. #4
    Super Member Quacky's Avatar
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    Re: Finding unknown variables

    Are you aware of the difference of two squares? We have two numbers, x and y. We are told they are multiplied by themselves, to give x^2 and y^2.
    We are told then that the difference of the new numbers is less than 10, so x^2-y^2<10
    Using the difference of 2 squares rule,
    (x+y)(x-y)<10
    We are told that the original difference was 1, so x-y=1
    This means that (x+y)(1)<10
    (x+y)<10
    We also know that x+y>7
    This means that
    7<x+y<10

    Assuming x and y are integers, this doesn't leave many options when x-y=1. What are the options?
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  5. #5
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    Re: Finding unknown variables

    We are looking at 4 and 5 ?
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  6. #6
    Super Member Quacky's Avatar
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    Re: Finding unknown variables

    I believe so.
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