how to prove x cube + y cube + Z cube - 3 X Y Z is equal to zero if x+ y+ z is equal to zero
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We know that x³ + y³ + z³ - 3xyz = ( x + y + z ) ( x² + y² + z² - xy + yz + zx ) Putting x + y + z = 0 on R.H.S .,
we get x³ + y³ + z³-3xyz=0
it's very easy
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