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Question

If x + 1x = 2cosθ, then x3 + 1x3 =


A

cos3θ

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B

2cos3θ

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C

12cos3θ

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D

13cos3θ

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Solution

The correct option is B

2cos3θ


We have x + 1x = 2cosθ,

Now x3 + 1x3 = (x+1x)3 - 3x1x(x+1x)

= (2cosθ)33(2cosθ)=8cos3θ6cosθ

=2(4cos3θ3cosθ)=2cos3θ.

Trick: Put x = 1 θ=0.

Then x3 + 1x3 = 2 = 2cos3θ.


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