Question

If x+y+z=0 show that
x+y+z=3xyz​

Answer 1

Explanation:

perhaps you mean

x^3+y^3+z^3 = 3xyz

because

x+y+z = 0

x^3 + y^3 + z^3 - 3xyz = (x + y + z )(x^2 + y^2 + z^2 -xy - yz - xz)

(this equation is an identity)

x^3 + y^3 + z^3 - 3xyz = (x + y + z )(x^2 + y^2 + z^2 -xy - yz - xz)

x^3 + y^3 + z^3 - 3xyz = (0)(x^2 + y^2 + z^2 -xy - yz - xz)

x^3 + y^3 + z^3 - 3xyz = 0

x^3 + y^3 + z^3 = 3xyz