If ω is a complex cube roots of unity and a, b, c are such that 1/a+ω + 1/b+ω + 1/c+ω = 2ω^2

Question

If ω is a complex cube roots of unity and a, b, c are such that \(\frac1{a + \omega} + \frac1{b + \omega} + \frac1{c+\omega} = 2\omega^2\) and \(\frac1{a + \omega^2} + \frac1{b + \omega^2} + \frac1{c+\omega^2} = 2\omega\), then \(\frac 1{a+1} +\frac 1{b+1} + \frac 1{c+1}\) =

(a) 1

(b) –1

(c) 2

(d) –2

Answer 1

Correct option is (c) 2