Question

if X + Y + Z is equals to zero show that x cube + y cube + Z cube is equals to 3 x y z

Answer 1

GIVEN:- x=y=z=0
Then,
x^3 + y^3 +z^3-3xyz = (x+y+z)(x^2+y^2+z^2-xy-yz-zx)
so, x+y+z=0
x^3+y^3+z^3-3xyz=0
x^3+y^3+z^3=3xyz

Answer 2

x+y+z=0
x+y=-z
cubing both the sides.
(x+y)^3=(-z)^3
x^3+y^3 +3xy(x+y)= -z^3
x^3+y^3 +3xy(-z)=-z^3 (x-y= -z)
x^3+y^3 -3xyz=-z^3
x^3+y^3+z^3=3xyz


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