Solve, when I already know 1 solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg73080] Solve, when I already know 1 solution*From*: DOD <no at none.com>*Date*: Thu, 1 Feb 2007 03:51:30 -0500 (EST)

I am trying to solve the following system of equations for, X, Y, and Z: {X((16 X ^3 - 39 X ^2 Y + 5 X Y ^2 + 8 Y ^3 + ((19 X ^2 - 10 X Y + 3 Y ^2) ) Z + 3 ((X + Y) ) Z ^2 + Z ^3) ) == 9 c, X Y ((29 X ^2 - 2 Y ((4 Y + Z) ) - 2 X ((9 Y + 5 Z) )) ) == (-9 ) c, Z ((10 X ^3 + 81 Y (Y - Z) ( (-1 ) + Z) + X Y ((81 - &9 Y + 2 Z) ) + X ^2 (( (- 81 ) + 72 Y + 4 Z))) ) == 9 c} (sorry for the bad formatting, I don't know a convenient way to copy this info from mathematica. Anyway, the precise polynomial isn't important. ) I would like a symbolic solution in c. So Solve chews on this forever without giving a solution. Now, it so happens that I already know a solution is X=Y=Z =c^(1/4), and I strongly suspect that all the other solutions, real or imaginary, are of the form X=q c^(1/4),Y=r c^(1/4),Z= s c^(1/4), for some (q,r,s). Is there any way I can use this info to help Solve along, and give me all the solutions? -- DOD

**Follow-Ups**:**Re: Solve, when I already know 1 solution***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>