Let α,β be the roots of x2−2xcos⁡ϕ+1=0  then the equation whose roots are αn and βn is

Let α,β be the roots of x22xcosϕ+1=0  then the equation whose roots are αn and βn is

  1. A

    x22xcos1=0

  2. B

    x22xcos+1=0

  3. C

    x22xsin+1=0

  4. D

    x2+2xsin1=0

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    The given equation is  x22xcosϕ+1=0
     x=2cosϕ±4cos2ϕ42=cosϕ±isinϕ
     Let α=cosϕ+isinϕ, then β=cosϕisinϕ  αn+βn=(cosϕ+isinϕ)n+(cosϕisinϕ)n           =2cosnϕ  and αnβn=(cosnϕ+isinnϕ)(cosnϕisinnϕ)=cos2nϕ+sin2nϕ=1
     Required equation is
    x22xcos+1=0

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.