Question 647301
<pre>
x² + y² + z² - xy - yz - zx - yz = 0 then prove that x = y = z

That isn't true. For here is a counter-example:

x = 0, y = 1, z = 1

0² + 1² + 1² - 0y - 1·1 - 1·0 - 1·1 = 0

0 +  1  + 1  -  0 -   1 -   0 -   1 = 0

                                  0 = 0

Maybe there was a typo, since there are two like 
terms -yz and -yz that immediately combine to give -2yz.
It seems strange that as advanced a problem as this would
leave something undone as elementary as requiring two like terms
to be combined.  Thus I suspect there was a typo.  If so,
you can correct it in the thank-you note.

Edwin</pre>