Question

If x+y+z=0, show that x*x*x+y*y*y+z*z*z=3xyz

Answer 1

x+y+z = 0
x+y = (-z)
Cubing on both sides
x^3+y^3+3xy(x+y) = (-z^3)
x*x*x + y*y*y + 3xy(-z) = (-z*z*z)
x*x*x+y*y*y+z*z*z=3xyz

Answer 2

X+y+z=0
Show that x³+y³+z³=3xyz
So
By formula
A+b+c=0 then a³+b³+c³=3abc

It is prove

I hope this will help you
By DEVANSH