JEE Advanced2011MathematicsQuadratic EquationActual

Let and be the roots of x^2-6 x-2=0 with > . If a_n= ^n- ^n for n 1 , then the value of a₁₀-2 a₈ 2 a₉ is

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Correct answer

C. 3

Step-by-step solution

a₁₀-2 a₈ 2 a₉ = ( ¹⁰- ¹⁰ )-2 ( ^8- ^8 ) 2 ( ^9- ^9 ) = ^8 ( ^2-2 )- ^8 ( ^2-2 ) 2 ( ^9- ^9 ) [ . is root of x^2-6 x-2=0 . ^2-2=6 ] Also, is root of x^2-6 x-2=0 aligned & ^2-2=6 & = ^8(6 )- ^8(6 ) 2 ( ^9- ^9 ) = 6 ( ^9- ^9 ) 2 ( ^9- ^9 ) =3 aligned

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