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Question

lf x2+x+1=0, then the value of
(x+1x)+(x2+1x2)++(x52+1x52) equals

A
1
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B
0
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C
1
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D
52
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Solution

The correct option is B 1
ω and ω2 are the roots of the given equation.
We have,
x+1x=ω+ω2=1
x2+1x2=ω2+ω=1
x3+1x3=2
This pattern will repeat after an interval of three terms. Hence, the sum of the given series is the last term.
Sum =1

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