VITEEE 2015 Paper

Given equation is x2 + x + 1 = 0
⇒ x = ω and x = ω2
Case I : When x = ω
Then

6

Σ

n=1

[xn+

1

xn

]2 =

6

Σ

n=1

[ω2+ω2n]2 [Since 1/ω = ω2]
= (ωω2)2+(ω2+ω4)2 + (ω3+ω6)2+(ω4+ω8)2 + (ω5+ω10)2 + (ω6+ω12)2
= 9−1)2+(−1)2+(2)2+(−1)2 + (−1)2+(2)2 = 12
Case II: When x = ω2
Then

6

Σ

n=1

[xn+

1

xn

]2 =

6

Σ

n=1

[ω2+ω2n]2 [Since 1/ω2 = ω] = 12