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

```

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