# How to solve this system of equations?

Posted 8 years ago
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 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:
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Posted 8 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}] 
Posted 8 years ago
 FindRoot only gives one solution for a given starting point. If you want more solutions, you should try more starting points.