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cubic equation solver

• To: mathgroup at smc.vnet.net
• Subject: [mg130242] cubic equation solver
• From: Elim Qiu <elim.qiu at gmail.com>
• Date: Thu, 28 Mar 2013 04:06:39 -0400 (EDT)
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• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
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x^3 + (=E2=88=9A6 + 2=E2=88=9A3 + 2=E2=88=9A2 -9)x + 2=E2=88=9A3 -=E2=88=9A2 -2 = 0
has exact roots =E2=88=9A2-2, =E2=88=9A3-=E2=88=9A2, 2-=E2=88=9A3

But Mathematica says:

Solve[x^3 + (Sqrt[6] + 2 Sqrt[3] + 2 Sqrt[2] - 9) x + 2 Sqrt[3] -
   Sqrt[2] - 2 == 0, x]

{{x -> (1/
      2 (18 + 9 Sqrt[2] - 18 Sqrt[3] +
        I Sqrt[3 (4662 - 1252 Sqrt[2] - 1296 Sqrt[3] -
            264 Sqrt[6])]))^(1/3)/3^(
    2/3) - (-9 + 2 Sqrt[2] + 2 Sqrt[3] + Sqrt[
     6])/(3/2 (18 + 9 Sqrt[2] - 18 Sqrt[3] +
        I Sqrt[3 (4662 - 1252 Sqrt[2] - 1296 Sqrt[3] -
            264 Sqrt[6])]))^(
    1/3)}, {x -> -(((1 + I Sqrt[3]) (1/
        2 (18 + 9 Sqrt[2] - 18 Sqrt[3] +
          I Sqrt[3 (4662 - 1252 Sqrt[2] - 1296 Sqrt[3] -
              264 Sqrt[6])]))^(1/3))/(
     2 3^(2/3))) + ((1 - I Sqrt[3]) (-9 + 2 Sqrt[2] + 2 Sqrt[3] +
       Sqrt[6]))/(
    2^(2/3) (3 (18 + 9 Sqrt[2] - 18 Sqrt[3] +
         I Sqrt[3 (4662 - 1252 Sqrt[2] - 1296 Sqrt[3] -
             264 Sqrt[6])]))^(
     1/3))}, {x -> -(((1 - I Sqrt[3]) (1/
        2 (18 + 9 Sqrt[2] - 18 Sqrt[3] +
          I Sqrt[3 (4662 - 1252 Sqrt[2] - 1296 Sqrt[3] -
              264 Sqrt[6])]))^(1/3))/(
     2 3^(2/3))) + ((1 + I Sqrt[3]) (-9 + 2 Sqrt[2] + 2 Sqrt[3] +
       Sqrt[6]))/(
    2^(2/3) (3 (18 + 9 Sqrt[2] - 18 Sqrt[3] +
         I Sqrt[3 (4662 - 1252 Sqrt[2] - 1296 Sqrt[3] -
             264 Sqrt[6])]))^(1/3))}}

• Follow-Ups:
  • Re: cubic equation solver
    • From: Bob Hanlon <hanlonr357@gmail.com>