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Re: Different answers in mathematica and my calculator.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125586] Re: Different answers in mathematica and my calculator.
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Tue, 20 Mar 2012 02:20:11 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201203191000.FAA01033@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

-1 has three cube roots, so your expression has three possible results,  
all of them correct:

Solve[x^3 == -1, x]
% // ComplexExpand
4/(3 x) /. %

{{x -> -1}, {x -> (-1)^(1/3)}, {x -> -(-1)^(2/3)}}

{{x -> -1}, {x -> 1/2 + (I Sqrt[3])/2}, {x -> 1/2 - (I Sqrt[3])/2}}

{-(4/3), 4/(3 (1/2 + (I Sqrt[3])/2)), 4/(3 (1/2 - (I Sqrt[3])/2))}

Hence, it's not the least surprising if your calculator gives a different  
result than Mathematica.

I do think the Solve result above (before applying ComplexExpand) is less  
than ideal or complete since, as I said before, -1 has three cube roots,  
leaving two of the reported solutions ambiguous. Mathematica chooses a  
specific "branch" of the multivalued cube-root function.

Bobby

On Mon, 19 Mar 2012 05:00:46 -0500, Nile <thrasher300 at gmail.com> wrote:

> 4/(3Power[2(-2)+3, (3)^-1])
>
> I get -(4/3) (-1)^(2/3) in Mathematica but only -4/3 on my calculator.
>
>
> N[Sec[8/(8 Sqrt[2])]]/Degree to get Cos^-1 of 8/(8 Sqrt[2]) and it gives  
> me 75 deg instead of 45...
>
> I'm not sure what I'm doing wrong, I tried in Wolfram Alpha and it gives  
> me the same thing.
>
> Thank you.
>
> -Francis
>


-- 
DrMajorBob at yahoo.com



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