Question

if X + Y + Z =0......
show that :-
x³ + y³ + z³= 3xyz

Answer 1

solution is attached above.

Answer 2

Given -

x + y + z = 0

So,

x + y = - z ______( 1 )

Cubing both sides of ( 1 ), we get

( x + y )³ = ( - z )³

{ Using identity -

( a + b )³ = a³ + b³ + 3ab ( a + b ) }

x³ + y³ + 3xy ( x + y ) = - z³

x³ + y³ + 3xy ( - z ) = - z³ [ From ( 1 ) ]

x³ + y³ - 3xyz = - z³

x³ + y³ + z³ = 3xyz

Hence, proved.

^^"