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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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