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Question
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
Options
5
4
3
2
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Solution
In the given problem, we have to find the value of `x-1/x`
Given `x^3 - 1/x^3 = 14`
We shall use the identity `(a-b)^3 = a^3 -b^3-3ab (a-b)`
`(x-1/x)^3 = x^3 - 1/x^3 - 3 xx x xx 1/x(x-1/x)`
`(x = 1/x)^3 = x^3 - 1/x^3 -3 (x-1/x)`
Put `x- 1/x = y` we get,
`(y)^3 = x^3 -1/x^3 -3(y)`
Substitute y = 2 in above equation we get,
`(2)^3 = x^3 -1/x^3 - 3 (2) `
`8 = x^3 - 1/x^3 -6`
`8+6 = x^2 -1/x^3`
`14 = x^3 - 1/x^3`
The Equation `(y )^3 = x^3 - 1/x^3 -3(y)`satisfy the condition that `x^3 - 1/x^3 = 14`
Hence the value of `x - 1 /x`is 2
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