Re: Explicit solution to Root[]

• To: mathgroup at smc.vnet.net
• Subject: [mg58433] Re: [mg58407] Explicit solution to Root[]
• From: "David Park" <djmp at earthlink.net>
• Date: Sat, 2 Jul 2005 04:06:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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

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