If x^3+y^3+^3=3xyz, then the relation between x,y and z is (x+y+z). True or false?
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x^3 + y^3 + z^2 = 3xyz
x^3 + y^3 + z^3 - 3xyz = 0
(x+ y + z)(x^2 + y^2 + z^2-2 xy - 2yz - 2zx ) =0
so
x + y + z = 0
and
x^2 - 2xy + y^2 + z^2 - 2xz + z^2
= 0
(x - y)^2 + (y - z)^2= 0
so
x = y
y = z
there for
x = y = z
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