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Math Help - Finding ordered triples.

  1. #1
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    Finding ordered triples.

    Find all ordered triples (x,y,z) of real numbers which satisfy:

    (x+y)(x+y+z)=120
    (y+z)(x+y+z)=96
    (x+z)(x+y+z)=72
    Last edited by wannabebrainiac; June 4th 2012 at 11:42 AM.
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  2. #2
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    Re: Finding ordered triples.

    Hint: Add all equations.
    Thanks from wannabebrainiac
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  3. #3
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    Re: Finding ordered triples.

    Quote Originally Posted by wannabebrainiac View Post
    Find all ordered triples (x,y,z) of real numbers which satisfy:

    (x+y)(x+y+z)=120
    (y+z)(x+y+z)=96
    (x+z)(x+y+z)=72
    Can you solve this system?
     \begin{align*}X+Y&=120 \\Y+Z&=96 \\X+Z&=72\end{align*}
    Last edited by Plato; June 4th 2012 at 01:36 PM.
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  4. #4
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    Re: Finding ordered triples.

    D'oh! Just solve for x, y, and z. It's that easy and I didn't even see it?

    Thanks!
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  5. #5
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    Re: Finding ordered triples.

    Quote Originally Posted by wannabebrainiac View Post
    D'oh! Just solve for x, y, and z. It's that easy and I didn't even see it?

    Thanks!
    It is not that easy
    You now need to divide A where A^2=X+Y+Z
    The final answer looks \pm x,~\pm y,~\pm z
    Last edited by Plato; June 4th 2012 at 01:37 PM.
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  6. #6
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    Re: Finding ordered triples.

    I am a bit lost. What does the system in post #3 have to do with the original system?

    Quote Originally Posted by Plato View Post
    You now need to divide A where A^2=x+y+z
    What does "divide A" mean?

    Quote Originally Posted by Plato View Post
    The final answer looks \pm x,~\pm y,~\pm z
    It seems to me that there are only two triples that satisfy the original system.
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  7. #7
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    Re: Finding ordered triples.

    Quote Originally Posted by emakarov View Post
    I am a bit lost. What does the system in post #3 have to do with the original system?

    What does "divide A" mean?

    It seems to me that there are only two triples that satisfy the original system.
    You are correct there are only two triples. I realize that was misleading, sorry.

    When I types up the original the caps got changed. I will edit it.

    Then x=X/A,~y=Y/A,~z=Z/A where A^2=X+Y+Z  .

    Take a look at this.
    Last edited by Plato; June 4th 2012 at 01:50 PM.
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