A) \[-1,\,1+2\omega ,\,1+2{{\omega }^{2}}\]
B) \[-1,\,1-2\omega ,\,1-2{{\omega }^{2}}\]
C) \[-1,\,-1,\,-1\]
D) None of these
Correct Answer: B
Solution :
\[{{(x-1)}^{3}}=-8\Rightarrow x-1={{(-8)}^{1/3}}\] Þ \[x-1=-2,-2\omega ,-2{{\omega }^{2}}\] Þ \[x=-1,1-2\omega ,1-2{{\omega }^{2}}\] Trick: By inspection, we see that (b) satisfies the equation i.e, \[{{(-1-1)}^{3}}+8=0,{{(1-2\omega -1)}^{3}}+8=0\]\[{{(1-2{{\omega }^{2}}-1)}^{3}}+8=0\].
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