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Question

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
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B
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C
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D
1
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Solution

The correct option is A 2
Givenx2+x+1=0x=1ι32or1+ι32α=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=2AnswerOptionA

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