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Question
If \[x - \frac{1}{x} = 5\] ,find the value of \[x^3 - \frac{1}{x^3}\]
Solution
In the given problem, we have to find the value of `x^3 - 1/x^3`
Given `x- 1/x = 5`
We shall use the identity `(a- b)^3 = a^3 -b^3 - 3ab(a-b)`
Here putting, `x- 1/x = 5`,
`(x-1/x)^3 = x^3 -1/x^3 -3 (x xx 1/x)(x- 1/x)`
`(5)^3 = x^3 - 1/x^3 -3 (x xx 1/x) (x-1/x)`
`125 = x^3 - 1/x^3 - 3 (x - 1/x)`
`125 = x^3 -1 /x^3 - 3 xx 5 `
`125 = x^3 -1 /x^3 -15 `
`125 +15= x^3 -1 /x^3 `
`140 = x^3 -1 /x^3 `
Hence the value of `x^3 -1 /x^3 ` is 140.
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