Question

If x+y+z=0, then find x^3+y^3+8​

Answer 1

Here is the Answer :-

x+y+z=0⇒x+y=−z

Cubing on both sides,

(x+y)^3 =(−z)^3

⇒ x^3+y^3 +3xy(x+y)=z^3

⇒x^3+y^3+3xy(−z)=−z^3

⇒x^3+y ^3−3xyz+z ^3=0

∴x ^3+y ^3 +z ^3=3xyz