Find The Value ? If

If 4a – 4/a +3=0, the the value of a3 – 1/a3 +3 is

  1. 3/16
  2.   -21/16
  3.   21/64
  4.   7/16
Desire Adnan Default Asked on 18th August 2015 in Maths.
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  • 1 Answer(s)

    Answer : (3) 21/64

    Explanation:-

    4 a – 4/a + 3 = 0
    Both side divide by 4,
    Then, a – 1/a + 3/4 = 0
    a – 1/ a = – 3/ 4            ………….. (1)
    Cube on both side,
    (a – 1/a)3 = (-3/4)3
    Formula-
    (a – b)3 = a3 – b3– 3 ab (a – b)
    Then, a3 – 1/a3 – 3 a x 1/a (a – 1/a) = – 27/64
    a3 – 1/a3 – 3 (-3/4) = – 27/64                  (from equation 1)
    a3 – 1/a3 + 9/4 = – 27/64
    a3 – 1/a3 = – 27/64 – 9/4
    a3 – 1/a3 = (- 27 – 9 x 16)/64
    a3 – 1/a3 = (- 27 – 144) / 64
    a3 – 1/a3 = – 171/64
    Add 3 on both side,
    a3 – 1/a3 + 3 = – 171/64 + 3
    a3 – 1/a3 + 3 = (-171 + 3 x 64)/64
    a3 – 1/a3 + 3 = (- 171 + 192)/64
    a3 – 1/a3 + 3 = 21/64
    Then, the value of a3 – 1/a3 + 3 is 21/64
    Hence, the answer is (3) 21/64.

    Anurag Mishra Professor Answered on 21st August 2015.
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