Question

solve this .......☺️

Answer 1

The answer is Option (c) = -1.

Hope the answer in the attachment helps!

Answer 2

Given,

$\frac{a + b\omega + c\omega^{2}}{b + c\omega + a\omega^{2}} \ \ + \frac{a + b\omega +c\omega^{2}}{c + a\omega + b\omega^{2}} \\ \\ = \frac{a\omega^{3} + b\omega + c\omega^{2}}{b + c\omega + a\omega^{2}} \ \ + \frac{a + b\omega +c\omega^{2}}{c\omega^{3} + a\omega + b\omega^{2}} \\ \\ = \frac{\omega(a\omega^{2} + b + c\omega)}{b + c\omega + a\omega^{2}} \ \ + \frac{a + b\omega +c\omega^{2}}{\omega(c\omega^{2} + a + b\omega)} \\ \\ = \omega + \frac{1}{\omega} \\ \\ = \frac{\omega^{2} +1}{w} \\ \\ = \frac{-w}{w} \\ \\ = -1 \\ \\ \\ \\ Note:1. \ \ \ 1 + \omega + \omega^{2} = 0 \\ \\ 2 . \ \ w^{3} = 1$