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Solving System of Equations - Critical Points

  1. Dec 11, 2016 #1
    1. The problem statement, all variables and given/known data

    5088ee9ada.png

    Hi,
    I seem to have this issue with solving the a system of 3 equations when trying to find the critical points for a 3 variable function.

    2. Relevant equations


    3. The attempt at a solution
    It always keeps happening. I keep getting stuck when solving these equations. Every single question has its own little trick in it on how to solve these equations

    f2c020bd74.jpg

    Any ideas? I need to do this as the first part in solving my question. I need to find the critical points then use the second derivative test to determine the type of critical points. I keep going around and around with equations, trying to fit them into other ones and it leads me nowhere.
     
  2. jcsd
  3. Dec 12, 2016 #2
    why is it that in your working
    yz = 1/(2 x^2) becomes y = z/(2 x^2)
    similarly
    xz = 1 /(y^2) becomes x=z/(y^2)
    and
    xy=2/z^2 becomes x = 2y/z^2

    it it that i am missing something or is it did you make a mistake?
     
  4. Dec 12, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    They are all mistakes.
     
  5. Dec 12, 2016 #4
    Oops. seems like i forgot some basic algebra. Give me a second ill fix that up.
     
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