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Math Help - solving big equation...stuck

  1. #1
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    Unhappy solving big equation...stuck

    I need to find ALL INTEGER solutions for
    0 = 67291851x^2 + 337901589xy − 79475826y^2 − 74334x + 1287y + 3



    i think i broke it down correctly, but stuck

    = (2823x + 14811y − 3)(23837x − 5366y − 1)

    need (x,y) solutions
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  2. #2
    Super Member Bacterius's Avatar
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    If you broke it down correctly then you are left with :

    2823x + 14811y - 3 = 0
    23837x - 5366y - 1 = 0

    (Then solve the system)

    EDIT : how could I not think about system of equations ? I lack imagination so badly ...
    Last edited by Bacterius; November 11th 2009 at 04:49 PM.
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  3. #3
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    Hello, AwesomeDesiKid!

    Find all integer solutions for:
    67291851x^2 + 337901589xy - 79475826y^2 - 74334x + 1287y + 3 \:=\:0

    i think i broke it down correctly, but stuck:

    . . (2823x + 14811y - 3)(23837x - 5366y - 1) \:=\:0

    Need (x,y) solutions.

    Set each factor equal to zero and solve the system of equations.
    (And hope there are integer solutions.)

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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Soroban View Post
    Hello, AwesomeDesiKid!


    Set each factor equal to zero and solve the system of equations.
    (And hope there are integer solutions.)

    The solution set (that is the set of all integer solutions) is S_1 \cup S_2 where S_1 is the solution set of:

    (2823x + 14811y - 3)=0

    and S_2 is the solution set of:

    (23837x - 5366y - 1)=0

    CB
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    The solution set (that is the set of all integer solutions) is S_1 \cup S_2 where S_1 is the solution set of:

    (2823x + 14811y - 3)=0

    and S_2 is the solution set of:

    (23837x - 5366y - 1)=0

    CB
    thats the hard part
    i been trying to do that for a while and i still haven't figured out how to do it
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AwesomeDesiKid View Post
    I had the original Equation as
    0 = 67291851X^2 + 337901589xy - 79475826y^2 - 74334x + 1287y + 3
    i split it in to
    0 = (2823x + 14811y - 3)(23837x - 5366y -1)
    then i got

    1 = 914x + 4937y
    1 = 23837x - 5366y
    but i can't slove it, cause i need a x and y as an integers
    any help
    Nice job factoring. I have no idea how you did that.

    You aren't going to get a set (x, y) for these. From the first factor you get
    0 = 2823x + 14811y - 3

    y = -\frac{2823}{14811}x + \frac{3}{14811}
    (I'll let you take care of the cancellations.)

    This linear relationship gives you a list of zeros of this equation. The other factor gives you a similar solution.

    You may, of course, pick out a specific zero. For example, we can pick out x = 0 and we have the zero
    \left ( 0, \frac{3}{14811} \right )

    -Dan
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  7. #7
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    Quote Originally Posted by AwesomeDesiKid View Post
    I had the original Equation as
    0 = 67291851X^2 + 337901589xy - 79475826y^2 - 74334x + 1287y + 3
    i split it in to
    0 = (2823x + 14811y - 3)(23837x - 5366y -1)
    then i got

    1 = 914x + 4937y
    1 = 23837x - 5366y
    but i can't slove it, cause i need a x and y as an integers
    any help
    If you're looking at solving your linear Diophantine equations, here's a site that might help

    LINEAR DIOPHANTINE EQUATIONS
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