Prove x³ + y³ +z³=3xyz.
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Genius0009:
it is not the complete question
If x + y + z =0
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Given
x+y+z=0. ------(1)
then
x+y= -z
cubing on both side
(x+y)^3= -z^3
formula =(x+y)^3= x^3+3xy(x+y)+ y^3
so here also
x^3+3xy(x+y)+y^3 = -z^3
x^3+3xy( -z)+y^3= -z^3
hence
x^3+ y^3+ z^3== 3xyz
proved
hope this helps
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