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Explicit solution to Root[]

• To: mathgroup at smc.vnet.net
• Subject: [mg58407] Explicit solution to Root[]
• From: "Mukhtar Bekkali" <mbekkali at gmail.com>
• Date: Fri, 1 Jul 2005 02:01:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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