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complex cube roots?

• To: mathgroup at smc.vnet.net
• Subject: [mg48101] complex cube roots?
• From: mathma18 at hotmail.com (Narasimham G.L.)
• Date: Thu, 13 May 2004 00:08:29 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Referring to my posted message  number 5 of same subject in
http://groups.google.co.in/groups?dq=&hl=en&lr=&ie=UTF-8&oe=ISO-8859-1&th=dfaed51b86703e8e
Solve[{x==a^3-3a b^2,y==3a^2 b-b^3},{a,b}]
brings out a long result, but can we not get the one real root to
Plot3D[{a,b,0},{x,-4,4},{y,-4,4}] ?