# Find The Value ? If

If 4a – 4/a +3=0, the the value of a^{3} – 1/a^{3} +3 is

- 3/16
- -21/16
- 21/64
- 7/16

**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} = a^{3} – b^{3}– 3 ab (a – b)

Then, a^{3} – 1/a^{3} – 3 a x 1/a (a – 1/a) = – 27/64

a^{3} – 1/a^{3} – 3 (-3/4) = – 27/64 (from equation 1)

a^{3} – 1/a^{3} + 9/4 = – 27/64

a^{3} – 1/a^{3} = – 27/64 – 9/4

a^{3} – 1/a^{3} = (- 27 – 9 x 16)/64

a^{3} – 1/a^{3} = (- 27 – 144) / 64

a^{3} – 1/a^{3} = – 171/64

Add 3 on both side,

a^{3} – 1/a^{3 }+ 3 = – 171/64 + 3

a^{3} – 1/a^{3} + 3 = (-171 + 3 x 64)/64

a^{3} – 1/a^{3} + 3 = (- 171 + 192)/64

a^{3} – 1/a^{3} + 3 = 21/64

Then, the value of a^{3} – 1/a^{3} + 3 is 21/64

Hence, the answer is (3) 21/64.