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AP EAMCET20225 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

, are the roots of x^2-10 x-8=0 with > . If _ n = ^ n - ^ n for n N , then the value of a₁₀-8 a₈ 5 a₉ is

Options

  1. A-3
  2. B3
  3. C-2
  4. D2

Correct answer

D. 2

Step-by-step solution

x^2-10 x-8=0 aligned & x^2-8=10 x & x^2-8 5 x =2 aligned , are roots ^2-8 5 =2 ^2-8=10 ...(i) ^2-8 5 =2 ^2-8=10 ...(ii) a₁₀-8 a₈ 5 a₉ = ¹⁰- ¹⁰-8 ( ^8- ^8 ) 5 ( ^9- ^9 ) aligned & = ( ¹⁰-8 ^8 )- ( ¹⁰-8 ^8 ) 5 ( ^9- ^9 ) & = ^8 ( ^2-8 )- ^8 ( ^2-8 ) 5 ( ^9- ^9 ) aligned Put, ^2-8=10 and ^2-8=10 From (i) and (ii) aligned & = ^8 10 - ^8 10 5 ( ^9- ^9 ) & = 10 ( ^9- ^9 ) 5 ( ^9- ^9 ) =2 aligned

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