Re: Explicit solution to Root[]

• To: mathgroup at smc.vnet.net
• Subject: [mg58449] Re: Explicit solution to Root[]
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 2 Jul 2005 04:07:13 -0400 (EDT)
• Organization: The Open University, Milton Keynes, England
• References: <da2mmv\$932\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Mukhtar Bekkali wrote:
> 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
>
> Mukhtar Bekkali
>
Hi Mukhtar,

Is this what you are looking for (*N* seems to work pretty well)?

In[1]:=
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]

Out[1]=
Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 +
54*#1^5 & , 1]

In[2]:=
N[%]

Out[2]=
1.1122081402235109

Best regards,
/J.M.

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