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JEE Main201911 Jan 2019Evening ShiftMathematicsQuadratic EquationActual

Let and be the roots of the quadratic equation x² -x( +1)+ =0 (0 < < 45^ ), and < . Then _ n=0 ^ ( ^ n + (-1)^ n ^ n ) is equal to :

Options

  1. A1 1- - 1 1+
  2. B1 1+ + 1 1-
  3. C1 1- + 1 1+
  4. D1 1+ - 1 1-

Correct answer

C. 1 1- + 1 1+

Step-by-step solution

x² -x( +1)+ =0 . x² -x -x+ =0x (x- )-1(x- )=0(x- )(x -1)=0 x= , cosec , (0,45^ ) = , = cosec _ n=0 ^ ^ n =1+ + ² + = 1 1- _ n=0 ^ (-1)^ n ^ n =1- 1 cosec + 1 cosec ² - 1 cosec ³ + =1- + ² - ³ + = 1 1+ _ n=0 ^ ( ^ n + (-1)^ n ^ n )= _ n=0 ^ ^ n + _ n=0 ^ (-1)^ n ^ n = 1 1- + 1 1+ .

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