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If and are the roots of the equation x^2-x+1=0 , then ²⁰⁰⁹+ ²⁰⁰⁹=

Options

  1. A-1
  2. B1
  3. C2
  4. D-2

Correct answer

B. 1

Step-by-step solution

x^2-x+1=0 x= 1 1-4 2 x= 1 3 i 2 = 1 2 +i 3 2 , = 1 2 - i 3 2 = 3 +i 3 , = 3 -i 3 ²⁰⁰⁹+ ²⁰⁰⁹=2 2009 ( 3 )=2 [668 + + 2 3 ]=2 ( + 2 3 )=-2 2 3 =-2 (- 1 2 )=1

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