Question

If 3a - (3/a) - 3 = 0. Then a^3 - (1/a^3) + 2=?

Answer 1

3a - 3/a - 3 = 0

=> a - 1/a - 1 = 0

=> a - 1/a = 1

On cubing both sides, we get

a^3 - 1/a^3 - 3(a)(1/a)(a-1/a) = 1

=> a^3 - 1/a^3 - 3(1) = 1

=> a^3 - 1/a^3 = 4

=> a^3 - 1/a^3 + 2 = 4 + 2

=> a^3 - 1/a^3 + 2 = 6

Answer 2

Given Equation is 3a - (3/a) - 3 = 0

It can be written as:

3(a - 1/a) - 3 = 0

 (a - 1/a) = 1

On cubing both sides, we get

= > (a - 1/a)^3 = 1

= > a^3 - 1/a^3 - 3(a - 1/a) = 1

= > a^3 - 1/a^3 - 3(1) = 1

= > a^3 - 1/a^3 = 4

= > a^3 - 1/a^3 = 4

Now,

a^3 - 1/a^3 + 2 = 4 + 2

                         = 6.



Hope this helps!