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 > commands would do the job? Please advise. Thanks, > > 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.