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MathGroup Archive 2005

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Re: Explicit solution to Root[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58418] Re: Explicit solution to Root[]
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 2 Jul 2005 04:06:14 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <da2mmv$932$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

a) RootReduce[] will simplify the expression a bit
   to
Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 + 
54*#1^5 & , 1, 0]

b) *this* is already a number, you can get a 
rational approximation or
   but this is the exact number.

Regards
  Jens




"Mukhtar Bekkali" <mbekkali at gmail.com> schrieb im 
Newsbeitrag news:da2mmv$932$1 at smc.vnet.net...
> Here is the code:
>
> \!\(\(Root[\(-2\)\ #1\^3 + 2\ #1\^4 - #1\ 
> Root[\(-4\) - 3\ #1 + 66\
> #1\^2 +
>          80\ #1\^3 - 108\ #1\^4 + 216\ #1\^5 &, 
> 1] - 6\ #1\^2\
> Root[\(-4\) - \
> 3\ #1 + 66\ #1\^2 + 80\ #1\^3 - 108\ #1\^4 + 
> 216\ #1\^5 &,
>                   1] + 6\ #1\^3\ Root[\(-4\) - 
> 3\ #1 +
>          66\ #1\^2 + 80\ #1\^3 - 108\ #1\^4 + 
> 216\ #1\^5 &, 1] - 5\ \
> Root[\(-4\) - 3\ #1 + 66\ #1\^2 + 80\ #1\^3 - 
> 108\ #1\^4 + 216\ #1\^5
> &, \
> 1]\^2 - 6\ #1\ Root[\(-4\) - 3\ #1 + 66\ #1\^2 + 
> 80\ #1\^3 - 108\ #1\^4
> +
>              216\ #1\^5 &, 1]\^2 + 6\ #1\^2\ 
> Root[\(-4\) - 3\ #1 +
>                  66\ #1\^2 + 80\ #1\^3 - 108\ 
> #1\^4 + 216\ #1\^5 &,
>                   1]\^2 - 2\ Root[\(-4\) -
>                3\ #1 + 66\ #1\^2 + 80\ #1\^3 - 
> 108\ #1\^4 + 216\ #1\^5
> &, 1]\
> \^3 + 2\ #1\ Root[\(-4\) - 3\ #1 + 66\ #1\^2 + 
> 80\ #1\^3 - 108\ #1\^4 +
> 216\ \
> #1\^5 &, 1]\^3 &, 2];\)\)
>
> I would guess it is a number.  I applied 
> RootReduce, ToRadicals, N or
> combinations of thereof, however, nothing seem 
> to convert the above
> expression into an explicit number. What command 
> or sequence of
> commands would do the job? Please advise. 
> Thanks,
>
> Mukhtar Bekkali
> 



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