If\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=k(x+y+z)\] \[\{{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}\}\], find\[k\].

If\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=k(x+y+z)\] \[\{{{(x-y)}^{2}}+{{

1.	If\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=k(x+y+z)\] \[\{{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}\}\], find\[k\].
A.	\[1\]
B.	\[\frac{1}{4}\]
C.	\[\frac{1}{2}\]
D.	\[\frac{1}{3}\]
Answer» D. \[\frac{1}{3}\]

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If\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=k(x+y+z)\] \[\{{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}\}\], find\[k\].

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