1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solve system equations
Loading...