       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

```

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