Mathematics - Determinant Question with Solution | TestHub

MathematicsDeterminantMiscellaneousMedium2 minPYQ_2024

MathematicsMediumsingle choice

If $x$ is a complex root of the equation $1 x x x 1 x x x 1 + 1 - x 11 1 1 - x 1 11 1 - x = 0$ , then $x^{2007} + x^{- 2007} =$

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Answer:

Solution:

Expanding the two determinants, we get $(1 - 3 x^{2} + 2 x^{3}) + (3 x^{2} - x^{3}) = 0$ $\Rightarrow x^{3} + 1 = 0$ $\Rightarrow x = - ω, - ω^{2}, - 1$ $x^{2007} + x^{- 2007} = - 1 - 1 = - 2$

Stream:BITSATSubject:MathematicsTopic:DeterminantSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2024

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