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Question
If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.
Sum
Solution
`5x + (1)/(5x) = 7`
Using `("a" + 1/"a")^3`
= `"a"^3 + (1)/"a"^3 + 3("a" + 1/"a")`, we get :
`(5x + 1/(5"x"))^3`
= `(5x)^3 + (1/(5x))^3 + 3(5x + 1/(5x))`
⇒ 343 = `125x^2 + (1)/(125x^3) + 3(7)`
⇒ `125x^3 + (1)/(125x^3)`
= 343 - 21
= 322.
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