if a,b,c are roots of x^3 -3x^2 + 3x +7 = 0 whee w is cube root of unity, then (a-1)/(b-1)+(b-1)/(c-1)+(c-1)/(a-1)=??

a. 3/w

b. w^2

c.2w^2

d 3w^2

The eqn is

 ( x - 1 ) ^3 = - 8

so a-1 , b-1 , c-1 =- 2 , -2w . -2w^2

Put the values

ans 3w^2

The roots of the eqn are -1,1-2w,1-2w².Therefore,the ans is

(-2/-2w)+(-2w/-2w²)+(-2w²/-2)=3/w

Sir,I think the values of a-1,b-1,c-1 are -2,-2w,-2w².But that doesn't make any diff as - gets cancelled.But the ans can well be 3/w or 3w² since w³=1.So,there are two options right.

Yaah !! now corrected .

Both are right .

ya u r correct but only 1 option mentioned in d book anywaz thanx 4 pointing out tat.....