Question

If x+y+z=0prove that x cube+y cube+z cube=3xyz

Answer 1

Answer:

x + y + z = 0

x + y = - z

cubing both sides

( x + y ) ^3 = ( - z )^3

x^3 + y^3 + 3xy(-z) = (-z)^3 ( x + y value taken from upside )

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

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

if x + y + z = 0 , then (x^3 + y^3 + z^3 ) = 3xyz