A) \[1\]
B) \[2\,\omega \]
C) \[2\,{{\omega }^{2}}\]
D) \[-1\]
Correct Answer: D
Solution :
\[\frac{a+b\omega +c{{\omega }^{2}}}{a{{\omega }^{2}}+b+c\omega }+\frac{a{{\omega }^{2}}+b\omega +c}{a+b{{\omega }^{2}}+c\omega }\] \[\frac{\omega (a+b\omega +c{{\omega }^{2}})}{(a{{\omega }^{2}}+b\omega +c{{\omega }^{2}})}+\frac{(a{{\omega }^{2}}+b{{\omega }^{2}}+c\omega )}{\omega \,(a+b{{\omega }^{2}}+c\omega )}\] \[=\omega +\frac{1}{\omega }\] \[=\frac{{{\omega }^{2}}+1}{\omega }=-\frac{\omega }{\omega }=-1\] \[(\because \,\,{{\omega }^{2}}+1=-\omega )\]
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