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Question

If α,β,γ are the roots of x3x21=0, then the value of 1+α1α+1+β1β+1+γ1γ=


A

- 5

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B

- 6

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C

- 7

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D

- 2

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Solution

The correct option is A

- 5


x3x21=0α+β+γ=1,αβ+βγ+γα=0,αβγ=1.
Now, 1+α1α=2(1α)1α=21α11+α1α=21α1=211α3 (i)Now,1xα+1xβ+1xγ=(xβ)(xγ)+(xα)(xβ)+(xα)(xγ)(xα)(xβ)(xγ)1xα+1xβ+1xγ=3x22xx3x21Let x=1=11α+11β+11γ=32111=1(i)=2(1)3=5


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