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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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>