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Question

If α and β are the roots of the equation x2-ax+b=0 andAn=αn+βn. Then An+1-aAn+bAn-1is equal to


A

-a

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B

b

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C

0

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D

a-b

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Solution

The correct option is C

0


Explanation for the correct option:

Find the value of An+1-aAn+bAn-1:

If α and β are the roots of the equation x2-ax+b=0, so each of them must satisfy the equation.

α2aα+b=0....(1) and β2aβ+b=0...(2)

Since An=αn+βn.

An+1aAn+bAn-1=αn+1+βn+1a(αn+βn)+b(αn-1+βn-1)An+1aAn+bAn-1=αn-1(α2aα+b)+βn-1(-aβ+b)An+1aAn+bAn-1=αn-1(0)+βn-1(0)An+1aAn+bAn-1=0

Hence the correct option is C.


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