       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
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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 + 2 Sqrt + 2 Sqrt - 9) x + 2 Sqrt -
Sqrt - 2 == 0, x]

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

```

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