A) \[-1,-1+2\omega ,-1-2{{\omega }^{2}}\]
B) \[-1,-1,-1\]
C) \[-1,1-2\omega ,1-2{{\omega }^{2}}\]
D) \[-1,1+2\omega ,1+2{{\omega }^{2}}\]
Correct Answer: C
Solution :
Given, \[{{(x-1)}^{3}}+8=0\] \[\Rightarrow \] \[{{(x-1)}^{3}}=-8\] \[\Rightarrow \] \[{{\left( \frac{x-1}{-2} \right)}^{3}}=1\] \[\Rightarrow \] \[\frac{x-1}{-2}={{(1)}^{1/3}}\] \[\Rightarrow \] \[\frac{x-1}{-2}=1,\omega ,{{\omega }^{2}}\] \[\Rightarrow \] \[x-1=-2,-2\omega ,-2{{\omega }^{2}}\] \[\Rightarrow \] \[x=-1,1-2\omega ,1-2{{\omega }^{2}}\]
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