Question

if x + y + z = 0 , show that x³ + y³ + z³ - 3xyz?

Answer 1

Hello friend
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= Put x + y + z = 0 ,
= x³ + y³ + z³ - 3xyz = ( 0 )  ( x² + y² + z² - xy - yz - zx )
= x³ + y³ + z³ - 3xyz = 0
= x³ + y³ + z³ = 3xyz
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Hope it will help u

Answer 2

x+y+z=0
x+y=-z
Cubing both sides 
(x+y)3 = (-z)3
(x)3+(y)3+3xy(x+y)= (-z)3
x+y=-z                  (SUBSTITUTING THE VALUE OF x+y)
(x)3+(y)3-3xy(z)+(z)3=0
(x)3+(y)3+(z)3=+3xyz