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Equation Solving

How to solve this system of equations?

Laurent Simula

Posted 10 years ago

Hi! I am trying to solve the system of equations in the attached file. What I am looking for are the values of tP and tC, both in (0,1), which satisfy: exp3= tP/(1 - tP) and exp6 = tC/(1 - tC) I am using FindRoot, but I have reasons to believe that it is not returning all the solutions. How would you solve this system of equations in Mathematica? Thanks a lot for your help. Laurent Attachments:

POSTED BY: Laurent Simula

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 10 years ago

I have some doubts that there are more than one solution, at least in the unit square. The following plots show ony one likely candidate: Plot3D[{Sqrt@Norm[{exp3 - tP/(1 - tP), exp6 - tC/(1 - tC)}], 0}, {tC, 0, 1}, {tP, 0, 1}, PlotRange -> {-.1, 1}, AxesLabel -> Automatic] Plot3D[{Sqrt@Norm[{exp3 - tP/(1 - tP), exp6 - tC/(1 - tC)}], 0}, {tC, .8, .9}, {tP, 0.5, .9}, PlotRange -> {-.1, 1}]

I have some doubts that there are more than one solution, at least in the unit square. The following plots show ony one likely candidate:

Plot3D[{Sqrt@Norm[{exp3 - tP/(1 - tP), exp6 - tC/(1 - tC)}], 0}, {tC, 
  0, 1}, {tP, 0, 1}, PlotRange -> {-.1, 1}, AxesLabel -> Automatic]
Plot3D[{Sqrt@Norm[{exp3 - tP/(1 - tP), exp6 - tC/(1 - tC)}], 
  0}, {tC, .8, .9}, {tP, 0.5, .9}, PlotRange -> {-.1, 1}]

POSTED BY: Gianluca Gorni

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 10 years ago

FindRoot only gives one solution for a given starting point. If you want more solutions, you should try more starting points.

POSTED BY: Frank Kampas

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