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