If a2 + 1 = a, then the value of a12 + a6 + 1 is

  1. 2
  2. 3
  3. -3
  4. 1
Anurag Mishra Professor Asked on 1st August 2015 in Maths.
Add Comment
  • 2 Answer(s)
    Best answer

    Answer: (2) 3
    Explanation:-
    a2 + 1 = a
    Both side divide by a,
    a2/a + 1/a = a/a
    a + 1/a + 1
    On squaring of both sides,
    (a + 1/a)2 = 12
    a2 + 1/a2 + 2 x a x 1/a = 1
    a2­ + 1/a2 + 2  = 1
    a2 + 1/a2 = 1 – 2 = -1                                …………………….. (1)
    On cubing of both sides,
    (a2 + 1/a2 )3 = ( – 1)3
    (a2)3 + (1/a2)3  + 3 x a2 x 1/a2 (a2 + 1/a2) = (-1) x (-1) x (- 1)
    a6 + 1/a6 + 3(a2 + 1/a2) = – 1
    a6 + 1/a6 + 3 (-1) = – 1
    a6 + 1/a6 + 1 =  3                                     …………………….. [From equation (1)]
    (a12 + 1 + a6)/a6 = 3
    a12 + a6 + 1 = 3
    Hence, the answer is (2) 3.

    Anurag Mishra Professor Answered on 1st August 2015.
    Add Comment

    (a^12+1+a^6)/a^6=3
    a^12+1+a^6=3*a^6
    how it became 3 sir please explain……….

    sree Default Answered on 1st July 2016.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.