Question

If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`

Answer 1

`a- 1/a` = 3...............(Given)

Taking a cube on both sides,

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

`a^3 - 1/a^3 - 3( a - 1/a) = 27`..............[(a - b)³ = a³ - b³ -3ab(a - b)]

`a^3 - 1/a^3 - 3 × 3 = 27..............[a- 1/a = 3]`

`a^3 - 1/a^3 - 9 = 27`

`a^3 - 1/a^3` = 27 + 9

`a^3 - 1/a^3` = 36.