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Solve system equations

  1. Dec 15, 2008 #1
    Find all pairs [tex](x,y) \in R [/tex] such that :
    [tex]\frac{x^4-16}{8x}=\frac{y^4-1}{y}[/tex] and [tex] x^2-2xy+y^2=8[/tex]
     
  2. jcsd
  3. Dec 15, 2008 #2
    1) You should write "pairs [tex](x,y) \in R^2 [/tex]" or "[tex]x, y \in R[/tex]".

    2) What form do you need the answer in? Looking at those 4th powers and mixed terms, I'm guessing that there might not be a simple or intuitive solution for this.

    3) What work have you done on the problem so far?
     
  4. Dec 15, 2008 #3

    CRGreathouse

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    Mathematica finds 8 complex solutions.
     
  5. Dec 15, 2008 #4
    I'am a elemantary pupil so I don't know about complex number
    Could anyone give me a complete solution.
     
  6. Dec 15, 2008 #5
    Mathematica > my rough analysis of the problem.

    If there's only 8 solutions, you can probably find them all by trial and error. To prove that there are exactly 8 solutions, and you have accounted for them all probably requires you to do a little arguing.
     
  7. Dec 15, 2008 #6

    arildno

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    Rewrite your equations as:
    [tex]\frac{(x-2)(x+2)(x^{2}+4)}{8x}=\frac{(y-1)(y+1)(y^{2}+1)}{y},(x-y)^{2}=8[/tex]
    this ought to help a bit.
     
  8. Dec 15, 2008 #7
    thanks but it seems to be not necessary for this problem.
    Though by putting x=2z I had : [tex]\frac{z^4-1}{z}=\frac{y^4-1}{y}[/tex],cossidering the function [tex]f(x)=x^3-\frac{1}{x} [/tex] and its monotonousness ,there are still some troubles for example f(x) is not continous at x=0
     
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