Re: Algebra Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg7676] Re: [mg7624] Algebra Problem*From*: Allan Hayes <hay at haystack.demon.co.uk>*Date*: Thu, 26 Jun 1997 01:36:59 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

>From: ironwolfNO at SPAMdangerousgames.com (Robert McNally) >Subject: [mg7676] [mg7624] Algebra Problem Robert, For Mma, (-1)(1/3) is ComplexExpand[(-1)^(1/3)] 1/2 + (I Sqrt[3])/2 r2 =ComplexExpand[(-1)^(2/3)] -(1/2) + (I Sqrt[3])/2 Which gives 1/3 2/3 -9 + 9 (-1) + 18 (-1) as -9+9r1 +18 r2//Expand -(27/2) + (27 I Sqrt[3])/2 You can use an equivelent pair of equations - inlude the definition of the cube roots: Solve[{2u^2 + 3u - 9 == 0, u^3==x},x] {{x -> -27}, {x -> 27/8}} Allan Hayes hay at haystack.demon.co.uk http://www.haystack.demon.co.uk/training.html voice:+44 (0)116 2714198 fax: +44 (0)116 2718642 Leicester, UK **** Begin forwarded message: >From: ironwolfNO at SPAMdangerousgames.com (Robert McNally) >Subject: [mg7676] [mg7624] Algebra Problem >Organization: Somewhere Out There I am using Mathematica to study Algebra. When I solve the following equation from my textbook with Mathematica, it gives me this result: In[1]:= Solve[2x^(2/3) + 3x^(1/3) - 9 == 0] Out[1]= 27 {{x -> --}} 8 However, my textbook claims that -27 is also a solution. If I tell Mathematica to turn off its solution verification, it finds the other textbook solution: In[213]:= Solve[2x^(2/3) + 3x^(1/3) - 9 == 0, VerifySolutions -> False] Out[213]= 27 {{x -> -27}, {x -> --}} 8 When I ask Mathematica to substitute -27 for x in the equation, Mathematica only goes so far in simplifying the equation, but not far enough to determine if the left side is the same as the right side: In[2]:= 2x^(2/3) + 3x^(1/3) - 9 == 0 /. x -> -27 Out[2]= 1/3 2/3 -9 + 9 (-1) + 18 (-1) == 0 Now, I can see that the cube root of -1 is -1, and that the taking the square of -1 yields 1, and then taking the cube root of that also yields 1. So the equation should simplify to: -9 - 9 + 18 == 0 and then 0 == 0 which would indicate that -27 is indeed a solution. But I can't figure out how to get Mathematica to return similar results. Trying to force Mathematica to give a numerical answer, yields an imaginary, non-zero result: In[3]:= N[2x^(2/3) + 3x^(1/3) - 9 /. x -> -27] Out[3]= -13.5 + 23.3827 I which may explain why Mathematica rejects this solution. So, is Mathematica rejecting the solution -27 appropriately or not? Thanks in advance. ====================================================================== Robert McNally <mailto:ironwolfNO at SPAMdangerousgames.com> Visit <http://personalweb.lightside.com/pfiles/mcnally1.html> ---------------------------------------------------------------------- Finger for my PGP Key -- Protect Your Crypto-Rights! * Free Speech! Unsolicited Commercial E-Mail Sucks! * Visit http://www.vtw.org ======================================================================