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
