Question

Under what condition x3+y3+z3=3xyz​

Answer 1

Answer: (X+Y+Z) = 0

Explanation: 3x+3y+3z-3xyz = (x+y+z) (x²+y²+z²+2xy+2yz+2zx)

So in this case if (x+y+z)= 0 then automatically the rhs will be 0 and then -3xyz will shift from lhs to rhs. Hence verified.