lf n is a multiple of 6 and α,β are the roots of x2+x+1=0, then (1+α)−n+(1+β)−n=
A
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
−2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
−1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A2 Givenx2+x+1=0⇒x=−1−ι√32or−1+ι√32∴α=ωandβ=ω2whenω=cuberootofunity.Alsoletn=6pwhenpisanaturalnumber.∴(1+α)−n+(1+β)−n=(1+ω)−6p+(1+ω2)−6p=(ω2)−6p+(ω)−6p=(ω3)−4p+(w3)−3p=1+1=2Answer−OptionA