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Question
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^3 - 1/a^3 )`
Solution
`(a - 1/a)^3 = a^3 - 1/a^3 - 3( a - 1/a )`
⇒ `( a^3 - 1/a^3 ) = (a - 1/a)^3 + 3( a - 1/a )`
⇒ `( a^3 - 1/a^3 ) = (4)^3 + 3(4)` [ ∵ `a - 1/a = 4` ]
⇒ `( a^3 - 1/a^3 ) = 64 + 12 `
⇒ `( a^3 - 1/a^3 ) = 76`
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