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Topic: Real Surface?
Replies: 4   Last Post: Jul 5, 2005 9:11 PM

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Posts: 24
Registered: 12/13/04
Real Surface?
Posted: Jul 5, 2005 6:32 PM
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In a recent problem, for there to be a solution the following
condition must hold:

x^4 + y^4 + z^4 - x y z(x + y + z)=0

{x, y, z} must be real. I can find the trivial solution

x = t, y = t, z = t, all real t.

I believe this line is the only real form satisfying the
equation but how can I prove this.

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