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If x +y+z=0, the show thatx² + y² + 2² = 3 xyz |
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Answer» GIVEN x+y+z=0 ⟹x+y=−z Cubing on both SIDES (x+y) 3 =(−z) 3
⟹x 3 +y 3 +3x y+3xy 2 =−z 3
⟹x 3 +y 3 +3xy(x+y)=−z 3
⟹x 3 +y 3 +3xy(−z)=−z 3
⟹x 3 +y 3 −3XYZ=−z 3
⟹x 3 +y 3 +z 3 =3xyz |
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