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Q.

If α is a root of Z2-Z+1=0 then

α2014+1α2014+α2015+1α20152+ α2016+1α20163+α2017+1α20174+ α2018+1α20185=

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An Intiative by Sri Chaitanya

a

8

b

-5

c

3

d

5

answer is A.

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Detailed Solution

z2-z+1=0   z=-w  or - w2

Let  α=-w

α=-w    α2014=w2014=(w3)671·w=w

      α2015=-w2, α2016=w3=1, α2017=-w, α2018=w2

  α2014+1α2014+α2015+1α20152+α2016+1α20163+α2017+1α20174+α2018+1α20185

    w+1w+-w2-1w22+1+113+-w-1w4+w2+1w25 =-1+12+23+1-1=8

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If α is a root of Z2-Z+1=0 thenα2014+1α2014+α2015+1α20152+ α2016+1α20163+α2017+1α20174+ α2018+1α20185=