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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