Question

If x + y + z = 0, find the value of xº + y2 + z3.​

Answer 1

Answer:

x+y+z=0⇒x+y=−z

Cubing on both sides,

(x+y)3=(−z)3

⇒x3+y3+3xy(x+y)=z3

⇒x3+y3+3xy(−z)=−z3

⇒x3+y3−3xyz+z3=0

∴x3+y3+z3=3xyz