If x+y+z=0 then,prove that x³+y³+z³=3xyz
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X+y+z=0
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x+y+Z=0
x+y=-z
cubing both side
(x+y)cube= (-z)cube
x cube +y cube +3xy(x+y)= -z cube
x cube +y cube + 3xy × -z =-z cube
x cube + y cube -3xyz = -z cube
x cube + y cube + Z cube = 3xyz....
proved
x+y=-z
cubing both side
(x+y)cube= (-z)cube
x cube +y cube +3xy(x+y)= -z cube
x cube +y cube + 3xy × -z =-z cube
x cube + y cube -3xyz = -z cube
x cube + y cube + Z cube = 3xyz....
proved
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