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Question

If α and β are the roots of the equation 375x225x2=0, then limnnr=1αr+limnnr=1βr is equal to :

A
7116
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B
112
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C
29358
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D
21346
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Solution

The correct option is B 112
Given, α and β are the roots of the equation 375x225x2=0
Therefore α+β=(25375)=(25375)
and αβ=(2375)
limnnr=1αr+limnnr=1βr=limnnr=1(αr+βr)
=limn(α1+β1)+(α2+β2)+(α3+β3)++(αn+βn)
=(α+α2+α3+)+(β+β2+β3+
Here we have infinite G.P series therefore
=α1α+β1β=α+β2αβ1(α+β)+αβ
=25375+43751253752375=29348=112

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