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Symmetry helps! (Posted on 2016-10-26) Difficulty: 4 of 5
Solve the system of equations below, listing all un-ordered triplets of integers:

x^2 −(y+z+yz)x+ (y+z)yz = 0
y^2 −(z+x+zx)y+ (z+x)zx = 0
z^2 −(x+y+xy)z+ (x+y)xy = 0

See The Solution Submitted by Ady TZIDON    
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Solution re(2): my short solution....summing up Comment 7 of 7 |
(In reply to re: my short solution by Daniel)

You are right.

No need to show it 3 times (one quotes 0!  - don't know why)

for (x,y,z)=(-1,1,1) lhs =1^2-(-1-1+1)+(-2*1)=1+1-2

SYMMETRY HELPS,  so we add 2 additional triplets: (1,-1,1) AND (1,1,-1)

summing up:  (0,0,0), (1,1,1,), (-1,1,1,), (1,-1,1,), (1,1,-1,).


  Posted by Ady TZIDON on 2016-10-27 09:55:38
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