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if \: x + y + z = 0 \: then \: show \: that \: {x}^(3) + {y}^(3 ) + {z}^(3) = 3xyz



User Naman Gala
by
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1 Answer

7 votes

Answer:

Given

x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3 +y 3 +3x 2y+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

Explanation:

Hope it is helpful.....

User Raymondralibi
by
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