Re: Re: FindRoot

*To*: mathgroup at smc.vnet.net*Subject*: [mg98769] Re: [mg98744] Re: [mg98693] FindRoot*From*: Gerry Flanagan <flanagan at materials-sciences.com>*Date*: Sat, 18 Apr 2009 03:39:36 -0400 (EDT)*References*: <200904170830.EAA23546@smc.vnet.net>

After the solution below, maybe you'll want ComplexExpand[r] // Simplify Gerry F. Bob Hanlon wrote: > eqn = x^3 - 4 a^2 x - 2 a^3 == 0; > > r = Simplify[x /. Solve[eqn, x], a > 0] > > {((4*3^(1/3) + (9 + I*Sqrt[111])^ > (2/3))*a)/(3^(2/3)* > (9 + I*Sqrt[111])^(1/3)), > (I*(-12 + 4*I*Sqrt[3] + > I*3^(1/6)*(9 + I*Sqrt[111])^ > (2/3) + (27 + 3*I*Sqrt[111])^ > (2/3))*a)/(2*3^(5/6)* > (9 + I*Sqrt[111])^(1/3)), > ((12*I - 4*Sqrt[3] - > 3^(1/6)*(9 + I*Sqrt[111])^ > (2/3) - > I*(27 + 3*I*Sqrt[111])^(2/3))* > a)/(2*3^(5/6)*(9 + I*Sqrt[111])^ > (1/3))} > > Plot[r, {a, 0, 5}] > > > Bob Hanlon > > ---- Miguel <misvrne at gmail.com> wrote: > > ============= > Hi all, > How can I to find the reals roots of a cubic equation in simbolic > form: For example, > > Find the roots of > x^3-4a^2x-2a^3==0 > > where "a" is real and a>0. > > Thanks > > > > >

**References**:**Re: FindRoot***From:*Bob Hanlon <hanlonr@cox.net>