Question

Find the value of the given expression:

$\frac{a+b\omega +c{\omega }^2}{c+a\omega +b{w}^2}+\frac{a+b\omega +c{\omega }^2}{b+c\omega +a{\omega }^2}$

• A. $1$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is D $-1$

$\frac{a+bw+c{w}^2}{c+aw+b{w}^2}+\frac{a+bw+c{w}^2}{b+cw+a{w}^2}$

$=\frac{1}{w}\left\{\frac{(aw+b{w}^2+c{w}^3)}{c+aw+b{w}^2}\right\}+\frac{1}{w^2}\left\{\frac{a{w}^2+b{w}^3+c{w}^4}{b+cw+a{w}^2}\right\}$

$=\frac{1}{w}.1+\frac{1}{w^2}.1=w+w^2\left[\begin{array}{cc}1+w+w^2=0& \\ w^3=1& \end{array}\right]$

$=-1$