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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