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Question

If α and β are the roots of the equation 5x22x+1=0, then the value of α21+α+β21+β is equal to

A
110
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B
25
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C
110
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D
15
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Solution

The correct option is C 110
5x22x+1=0
α+β=25, αβ=15

Now, α21+α+β21+β
=α2(1+β)+β2(1+α)(1+α)(1+β)
=(α2+β2)+αβ(α+β)1+(α+β)+αβ
=(25)225+15×251+25+15
=110

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