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

Answers (1)
R Riya

We know that

x^3+y^3+z^3-3xyz = (x+y+z)(x^2+y^2+z^2-xy-yz-zx)

Now, It is given that  x + y + z = 0

Therefore,

x^3+y^3+z^3-3xyz =0(x^2+y^2+z^2-xy-yz-zx)

x^3+y^3+z^3-3xyz =0

x^3+y^3+z^3=3xyz

Hence proved 

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