If and are the roots of

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

\alpha, \beta

and

\gamma

are the roots of

x^3 - 3x^2 + 3x + 7 = 0

, find the value of

\frac{\alpha-1}{\beta-1} + \frac{\beta-1}{\gamma-1} + \frac{\gamma-1}{\alpha-1}