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Solving a system of 3 nonlinear equations

  1. Jan 23, 2013 #1
    a = xyz
    b = xy+xz+yz
    c = x + y + z

    How do you solve x, y, and z?
     
  2. jcsd
  3. Jan 23, 2013 #2

    mfb

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    x=c-y-z
    b=(c-y-z)y + (c-y-z)z + yz = c(y+z)-y^2-zy-z^2
    Solve this quadratic equation for y (or z), use both in a=xyz and hope that it has a nice solution?
     
  4. Jan 23, 2013 #3
    It is not a quadratic equation. And it is not a "nice" solution.

    I have determined that z^3-cz^2+bz-a = 0. So, if we can find the roots of the cubic function, then we have z as a function of a, b, and c. Then, it should be straightforward to find x and y in terms of a, b, and c.

    But I forget how to find the roots of a cubic function.
     
  5. Jan 23, 2013 #4

    mfb

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