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Question
If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.
Solution
`3x - (1)/(3x) = 9`
Using `("a" - (1)/"a")^3`
= `"a"^3 - (1)/"a"^3 - 3("a" - 1/"a")`, we get :
`(3x - 1/(3x))^3`
= `(3x)^3 - (1/(3x))^3 -3(3x - 1/(3x))`
⇒ 729 = `27x^3 - (1)/(27x^3) - 3(9)`
⇒ `27x^3 - (1)/(27x^3)`
= 729 + 27
= 756.
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