Question

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

Answer 1

x + y +z = 0

=> x + y = - z ---------(1)

On cubing both sides, we get

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

=> x^3 +y^3 +3xy (-z) = - z^3 (using equation 1)

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

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


Hence Proved.......