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Math Help - x,y equation

  1. #1
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    x,y equation

    x^2-6xy+3y^2=100 x,y are natural numbers.

    Help would be appreciated.
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  2. #2
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    Re: x,y equation

    Use the usual formula to solve as a quadratic in x.
    You need the term under the square root sign to be a perfect square.
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  3. #3
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    Re: x,y equation

    To add to bobP's comment, once you get your expression for a perfect square you are likely to need to use a spreadsheet to find the x values. At least I could find no pattern for the first 5 perfect squares.

    -Dan
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  4. #4
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    Re: x,y equation

    Wolfram Alpha gives a complete set of integer solutions. They look quite messy and I haven't checked them out in any way.
    The first few though are not difficult following the quadratic/discriminant route.
    You need 6y^{2}+100 to be a square, so check out the sequence 6y^{2}=21, 44, 69, 96,... .
    6y^{2}=96 gets you an early hit and a second comes not much further on.
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    Forum Admin topsquark's Avatar
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    Re: x,y equation

    Quote Originally Posted by BobP View Post
    Wolfram Alpha gives a complete set of integer solutions. They look quite messy and I haven't checked them out in any way.
    The first few though are not difficult following the quadratic/discriminant route.
    You need 6y^{2}+100 to be a square, so check out the sequence 6y^{2}=21, 44, 69, 96,... .
    6y^{2}=96 gets you an early hit and a second comes not much further on.
    I may have been using a more complicated system than you. (I had to define a z that was equal to the square root of the discriminant.) This is a rather common difficulty of mine.

    How did you code your question to Wolfram|Alpha? I tried to do that to check my work but was unable to get it to solve the problem

    -Dan
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  6. #6
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    Re: x,y equation

    I'm not a regular user of Wolfram Alpha, in fact this is the first time that I've actually asked it a question.
    I simply typed in the equation and pressed the compute button.
    It came back with a whole pile of stuff, including a graph, which was pleasing to see, and a section headed 'Integer Solutions '.
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