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Question

If α and β are the roots of x2+2x+2=0, then the value of (1α+2)3+(1β+2)3 is

A
14
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B
14
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C
12
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D
12
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Solution

The correct option is C 12
α and β are the roots of x2+2x+2=0
α2+2α+2=0 and β2+2β+2=0
1α+2=α2 and 1β+2=β2

Now, (1α+2)3+(1β+2)3
=(α2)3+(β2)3
=18(α3+β3)
=18(α+β)(α2αβ+β2)
=18(α+β)[(α+β)23αβ]
=18(21)[(2)23×2]
=12

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