Re: Problems with Solve
- To: mathgroup at smc.vnet.net
- Subject: [mg132475] Re: Problems with Solve
- From: Dana DeLouis <dana01 at icloud.com>
- Date: Wed, 26 Mar 2014 03:23:29 -0400 (EDT)
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- Delivered-to: l-mathgroup@wolfram.com
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On Sunday, March 23, 2014 5:01:17 AM UTC-4, totarefugium wrote: > Hello, > > In[1]:= N[Solve[z + 5 (z^2 - 1) + 1 z^3 == 1, z]] > > Out[1]= {{z -> 0.925423 + 0. I}, {z -> -4.47735 + 2.22045*10^-16 I}, {z > > -> -1.44807 - 4.44089*10^-16 I > > This equation has 3 real solutions. However, the answers returned when I ask mathematica for a decimal answer are complex (which I need to do later on when an integration needs solving numerically): > > > {{z -> 0.925423 + 0. I}, {z -> -4.47735 + > > > 2.22045*10^-16 I}, {z -> -1.44807 - 4.44089*10^-16 I}} (* A complex solution *) sol=z/.Solve[z+5 (z^2-1)+1 z^3==1,z]; sol//ComplexExpand//FullSimplify {1/3 (-5+Sqrt[22] Cos[1/3 ArcTan[(9 Sqrt[503])/43]]+Sqrt[66] Sin[1/3 ArcTan[(9 Sqrt[503])/43]]), 1/3 (-5-2 Sqrt[22] Cos[1/3 ArcTan[(9 Sqrt[503])/43]]), 1/3 (-5+Sqrt[22] Cos[1/3 ArcTan[(9 Sqrt[503])/43]]-Sqrt[66] Sin[1/3 ArcTan[(9 Sqrt[503])/43]])} N[%,25] 0.9254229177777078310769981, -4.477352348008969997944065, -1.448070569768737833132933