A) \[{{x}^{3}}+1\]
B) \[{{x}^{3}}+\omega \]
C) \[{{x}^{3}}+{{\omega }^{2}}\]
D) \[{{x}^{3}}\]
Correct Answer: D
Solution :
[d]: Let \[({{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}})\] \[=x[1\{(x+{{\omega }^{2}})(x+\omega )-1\}+\omega \{1-(x+\omega )\}\] \[+{{\omega }^{2}}\{1-(x+{{\omega }^{2}})\}]\] \[=x({{x}^{2}}+\omega x+{{\omega }^{2}}x+{{\omega }^{3}}-1+\omega -\omega x-{{\omega }^{2}}+{{\omega }^{2}}\] \[-{{\omega }^{2}}x-{{\omega }^{4}})={{x}^{3}}\] \[(\because {{\omega }^{3}}=1)\].You need to login to perform this action.
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