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Question

If x+y+z=0, what can be said about x3+y3+z3?

A
x3+y3+z3=0
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B
x3+y3+z3=3
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C
x3+y3+z3=3xyz
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D
x3+y3+z3=x2y+y2z+z2x
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Solution

The correct option is C x3+y3+z3=3xyz
We know,

x3+y3+z33xyz = (x+y+z) (x2+y2+z2xyyzzx)

x+y+z=0

We have,
x3+y3+z33xyz=0


x3+y3+z3=3xyz

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