2
$\begingroup$

if $\alpha$, $\beta$ and $\gamma$ are the roots of equation $x^3-3x^2+3x+7=0$ ($\omega$ is the cube root of unity),then

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

(a)$\frac{3}{{\omega}}$ (b) ${\omega}^2$ (c) 2${\omega}^2$ (d) 3${\omega}^2$

The question is from the IIT entrance Exam practice material. The Answer marked in the solution booklet is (a) but I am unable to find the way to get it. Please help me out.

Thanks in Advance.

$\endgroup$
9
$\begingroup$

Hint: If $\alpha,\beta,\gamma$ are the roots of $(x-1)^3+8=0$, what are $\alpha-1,\beta-1$ and $\gamma-1$ the roots of?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.