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AP EAMCET2013MathematicsQuadratic Equation

If and are the roots of the equation x^2-2 x+4=0 , then ^9+ ^9 is equal to

Options

  1. A-2^8
  2. B2^9
  3. C-2¹⁰
  4. D2¹⁰

Correct answer

C. -2¹⁰

Step-by-step solution

Given quadratic equation is x^2-2 x+4=0 whose roots are and . + =2 and =4 Now, aligned & ^9+ ^9= ( ^3 )^3+ ( ^3 )^3 & = ( ^3+ ^3 ) ( ^6+ ^6- ^3 ^3 ) = & ( + ) ( ^2- + ^2 ) [ ( ^2 )^3+ ( ^2 )^3- ^3 ^3 ] = & ( + ) [( + )^2-3 ] & [ ( ^2+ ^2 ) ( ^4+ ^4- ^2 ^2 )- ^3 ^3 ] = & ( + ) [( + )^2-3 ] [ ( + )^2-2 . & . ( ^2+ ^2 )^2-3 ^2 ^2 - ^3 ^3 ] = & ( + ) [( + )^2-3 ] [ ( + )^2-2 . & . [ ( + )^2-(2 ) ]^2-3 ^2 ^2 - ^3 ^3 ] = & 2[4-12] [ 4-8 (4-8)^2-48 -64 ] aligned [from Eq. (i)] aligned & =2(-8) (-4)(-32)(-64) & =2(-8)(128-

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