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Question
If `x - 1/x = 3`, then the value of `x^3 - 1/x^3` is ______.
Options
27
36
45
18
MCQ
Fill in the Blanks
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Solution
If `x - 1/x = 3`, then the value of `x^3 - 1/x^3` is 36.
Explanation:
Let’s solve step-by-step:
1. Given `x - 1/x = 3`, we want to find `x^3 - 1/x^3`.
2. We use the identity:
`(x - 1/x)^3 = x^3 - 1/x^3 - 3(x - 1/x)`
3. Substitute `x - 1/x = 3`:
`3^3 = x^3 - 1/x^3 - 3 xx 3`
`27 = x^3 - 1/x^3 - 9`
4. Rearrange to find `x^(3) - 1/x^3`:
`x^3 - 1/x^3 = 27 + 9`
`x^3 - 1/x^3 = 36`
Hence, the value of `x^3 - 1/x^3` is 36.
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