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Only one, one, one (Posted on 2007-05-30) Difficulty: 3 of 5
It's obvious that x=y=z=1 is an all-positive, all-real, solution of

x + y + z = 3
y + z + x = 3
z + x + y = 3

Can you prove that it is the only such solution?

See The Solution Submitted by Federico Kereki    
Rating: 4.5000 (4 votes)

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re: solution | Comment 4 of 5 |
(In reply to solution by Robby Goetschalckx)

With the substitution x = 1+d_x, y=1+d_y, z=1+d_z, the domain x>0, y>0, z>0 gets remapped to d_x>-1, d_y>-1, d_z>-1.
Your proof only goes as far as d_x>0, d_y>0, d_z>0, which only covers x>1, y>1, z>1, and does not rule out possibilities like 1>x>0.

  Posted by Brian Smith on 2007-05-31 15:11:55
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