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AP EAMCET202018 Sep 2020Morning ShiftMathematicsQuadratic EquationActual

If ( ) and ( ) are non-real roots of (x^3-x^2-x-2=0 ), then ( ²⁰²⁰+ ²⁰²⁰+ ²⁰²⁰ ²⁰²⁰= )

Options

  1. A1
  2. B2020
  3. C(1+ + )
  4. D-1

Correct answer

C. (1+ + )

Step-by-step solution

Given equation, (x^3-x^2-x-2=0 ) ( (x-2) (x^2+x+1 )=0 ) ( ) and ( ) are ( -1 3 i 2 ) or we can say ( ) and ( ) are non-real complex roots of unity. So, let ( = ) and ( = ^2 ), where ( ^3=1 ) and ( aligned & ^2+ +1=0. & ²⁰²⁰+ ²⁰²⁰+ ²⁰²⁰ ²⁰²⁰ & = ²⁰²⁰+ ⁴⁰⁴⁰+ ²⁰²⁰ ⁴⁰⁴⁰ & = ( ^3 )⁶⁷³ + ( ^3 )¹³⁴⁶ ^2+ ( ^3 )⁶⁷³ ( ^3 )¹³⁴⁶ ^2 & = + ^2+ ^3=1+ + ^2=1+ + . aligned )

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