lf xn=ωn+1ωn then x1x2x3...........x12=

xn=wn+1wnx1=w+1w=w+w2=-1, x2=w2+1w2=w2+w=-1x3=w3+1w3=2x1x2x3.....x12=x1x2x34=(-1) (-1) (2)4 =16

lf xn=ωn+1ωn then x1x2x3...........x12=

xn=wn+1wnx1=w+1w=w+w2=-1, x2=w2+1w2=w2+w=-1x3=w3+1w3=2x1x2x3.....x12=x1x2x34=(-1) (-1) (2)4 =16

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$lf x_{n} = ω^{n} + \frac{1}{ω^{n}} then x_{1} x_{2} x_{3} . . . . . . . . . . . x_{12} =$

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answer is C.

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Detailed Solution

$\begin{array}{rcl} x_{n} & = & w^{n} + \frac{1}{w^{n}} \\ x_{1} & = & w + \frac{1}{w} = w + w^{2} = - 1, x_{2} = w^{2} + \frac{1}{w^{2}} = w^{2} + w = - 1 \\ x_{3} & = & w^{3} + \frac{1}{w^{3}} = 2 \\ x_{1} x_{2} x_{3} . . . . . x_{12} & = & {(x_{1} x_{2} x_{3})}^{4} = {((- 1) (- 1) (2))}^{4} \\ = & 16 \end{array}$