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Re: Explicit solution to Root[]


Mukhtar,

N worked for me with Version 5.1.1.

expr = 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]; 

expr // N
1.11221

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 

From: Mukhtar Bekkali [mailto:mbekkali at gmail.com]
To: mathgroup 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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