if x+y+z=0 then x^3+y^3+z^3
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Answer : 3xyz
Step-by-step explanation:
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
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