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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2013 · Mathematics · Quadratic Equation

If α, β are the roots of the equation x^2+x+2=0 , then what is α^...

If α,β\alpha, \beta are the roots of the equation x2+x+2=0x^2+x+2=0, then what is α10+β10α−10+β−10\frac{\alpha^{10}+\beta^{10}}{\alpha^{-10}+\beta^{-10}} equal to?

Options

  1. A4096
  2. B2048
  3. C1024
  4. D512

Correct answer

C. 1024

Step-by-step solution

From given equation, α+β=−1\alpha+\beta=-1 and α⋅β=2α10+β10α−10+β−10=α10+β10α10+β10(α⋅β)10=(α⋅β)10=(2)10=1024\alpha \cdot \beta=2\frac{\alpha^{10}+\beta^{10}}{\alpha^{-10}+\beta^{-10}}=\frac{\frac{\alpha^{10}+\beta^{10}}{\alpha^{10}+\beta^{10}}}{(\alpha \cdot \beta)^{10}}=(\alpha \cdot \beta)^{10}=(2)^{10}=1024
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