[Date Index]
[Thread Index]
[Author Index]
Re: Algebra Problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg7642] Re: [mg7624] Algebra Problem
*From*: seanross at worldnet.att.net
*Date*: Tue, 24 Jun 1997 03:36:05 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Robert McNally wrote:
>
> 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
> ======================================================================
Mathematica has no built-in preference over which root to choose when
doing complex operations. Humans, on the other hand, tend to like real
numbers. (-27)^(1/3) has three answers as does (-27)^2/3. Two of those
roots are complex, one is real. The package 'RealOnly' in the standard
add-on packages may help you out. Instead of using the Solve command,
you could also check out Roots and FindRoots.
Prev by Date:
**Re: Replace expressions**
Next by Date:
**Re: Algebra Problem**
Previous by thread:
**Algebra Problem**
Next by thread:
**Re: Algebra Problem**
| |