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If x + y + z = 0, show that x^3 + y^3 + z^3 = 3xyz.

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If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.

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Best answer

x + y + z = 0 

x + y = -z 

by cubing on both sides, 

(x + y)3 = (-z)3 

x3+ y3 + 3xy(x + y) = -z3 

x3 + y3 + 3xy (-z) 

= -z (∵ x + y =-z data given) 

x3 + y3 – 3xyz = -z3 

∴ x3 + y3 + z3 = 3xyz.

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