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Question

Let α and β be the roots of x26x2=0. If an=αnβn for n1, then the value of a102a83a9 is:

A
1
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B
4
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C
2
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D
3
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Solution

The correct option is C 2
α and β be the roots of x26x2=0. So,
α26α2=0α22=6α
β26β2=0β22=6β
Now,
a102a83a9=(α10β10)2(α8β8)3(α9β9)
=(α102α8)(β102β8)3(α9β9)
=α8(α22)β8(β22)3(α9β9)
=α8(6α)β8(6β)3(α9β9)=6(α9β9)3(α9β9)=63=2

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