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Re: Numerical expression

• To: mathgroup at smc.vnet.net
• Subject: [mg128831] Re: Numerical expression
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 29 Nov 2012 06:05:26 -0500 (EST)
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• References: <20121128081654.7B2D168A1@smc.vnet.net>

You need to force the use of the real root rather than the principal
root for the cube root subexpressions

((9 (3)^(1/2) - 4 (23)^(1/2)))^(1/3) // N

0.765945 + 1.32666 I

Solve[a^3 == (9 (3)^(1/2) - 4 (23)^(1/2)), a] // N // Chop

{{a -> 0.765945 + 1.32666 I}, {a -> 0.765945 - 1.32666 I}, {a -> -1.53189}}

expr /. Solve[{
    expr == (a + b)/(3)^(1/2),
    a^3 == (9 (3)^(1/2) + 4 (23)^(1/2)),
    b^3 == (9 (3)^(1/2) - 4 (23)^(1/2))},
   {a, b, expr}, Reals][[1]]

1

expr /. (Reduce[{
      expr == (a + b)/(3)^(1/2),
      a^3 == (9 (3)^(1/2) + 4 (23)^(1/2)),
      b^3 == (9 (3)^(1/2) - 4 (23)^(1/2))},
     expr, Reals] // FullSimplify // ToRules)

1

I don't know why but WolframAlpha doesn't handle either of these
Mathematica expressions when input directly as above.


Bob Hanlon


On Wed, Nov 28, 2012 at 3:16 AM, Dana DeLouis <dana01 at me.com> wrote:
>> ( ( 9(3)^1/2+4(23)^1/2)^1/3 + (9(3)^1/2+4(23)^1/2)^1/3  )  /  (3)^1/2)
>
> Hi.   Just to add to the others, if we "Assume" the following
>
> k = (9*Sqrt[3] + 4*Sqrt[23])^ (1 / 3)  ;
>
> // Or...
> k=k//FullSimplify
> Sqrt[1/2 (13+Sqrt[69])]
>
>
> Then what you have is:
>
> (k+k) / Sqrt[3.]
>  3.76887
>
> // Which matches what others have mentioned:
>
> For this to equal 1,   then k would have to equal
>
> Sqrt[3] / 2
>
> Perhaps your equation for the k part is off a little. ??
>
> = = = = = = = = = =
> HTH  :>)
> Dana DeLouis
> Mac & Mathematica 8
> = = = = = = = = = =
>
>
>
>
> On Sunday, November 25, 2012 11:29:24 PM UTC-5, Massimo wrote:
>> How could I handle in Mathematica this expression?
>>
>>
>>
>> ( ( 9(3)^1/2+4(23)^1/2)^1/3 + (9(3)^1/2+4(23)^1/2)^1/3  )  /  (3)^1/2)
>>
>>
>>
>> With a lot of trouble I have found out that is equal 1,
>>
>> but how to get it with Mathematica?
>>
>>
>>
>> Thanks very much.
>>
>>
>>
>>
>>
>>
>>
>> __________ Informazioni da ESET Smart Security, versione del database =
> delle firme digitali 7729 (20121125) __________
>>
>>
>>
>> Il messaggio =EF=BF=BD stato controllato da ESET Smart Security.
>>
>>
>>
>> www.nod32.it
>
>
>
>
>

• References:
  • Re: Numerical expression
    • From: Dana DeLouis <dana01@me.com>