JEE Mains Model Paper 25

From the given equation, we have
(y−1)3 = -27 ⇒ (

y−1

−3

)3 = 1
∴

y−1

−3

= (1)1∕3
∴

y−1

−3

= 1 , ω , ω2
As a, b, c are the roots of the given equation,
∴ a - 1 = -3 , b - 1 = -3ω , c - 1 = -3ω2
∴

a−1

b−1

+

b−1

c−1

+

c−1

a−1

=

1

ω

+

1

ω

+

ω2

ω3

= ω2+ω2+ω2 = 3 ω2