Question

If p,q,r are roots of the equation x^3+3x^2+3x+7=0 and w is complex cube roots of unity find the value of
$\frac{p - 1}{q - 1} + \frac{q - 1}{r - 1} + \frac{r - 1}{p - 1}$
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Answer 1

We have x3 − 3x2 + 3x + 7 = 0 ⇒ (x − 1)3 + 8 = 0 ⇒ (x − 1)3 = (−2)3 = 1, ω, ω2 (cube roots of unity)

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