Let x, y, z be positive reals. Which of the following implies x = y = z?
(I) x3 + y3 + z3 = 3xyz
(II) x3 + y2 z + yz2 = 3xyz
(III) x3 + y2 z + z2 x = 3xyz
(IV) (x + y + z)3 = 27xyz
I, II, IV only
For option (3) if x = z = 1 and y = 2 then option (3) is right.
So by option (3) we can’t say x = y = z. Remaining options implies x = y = z.