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Question

If α and β are the roots of the equation x2-7x+1=0, then the value of 1/(α-7)2+1/(β-7)2 is


A

45

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B

47

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C

49

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D

50

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E

51

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Solution

The correct option is B

47


Explanation for the correct option:

Find the value of 1/(α-7)2+1/(β-7)2 :

Given that α and β are the roots of the equation x2-7x+1=0.

(α+β)=7;α.β=1

and α7=β;β7=α

Now, 1/(α-7)2+1/(β-7)2

=1(-β)2+1(-α)2=1β2+1α2=α2+β2(α.β)2=α2+β2+2α.β-2α.β(α.β)2=(α+β)2-2α.β(α.β)2=49-21=47

Hence, the correct option is (B).


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