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Questions
If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.
If `(x^2 + 1)/x = 3 1/3 "find" x - 1/x`.
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Solution
Given `(x^2 + 1)/x = 3 1/3`
`(x^2 + 1)/x = 10/3`
`x + 1/x = 10/3`
Squaring on both sides, we get
= `(x + 1/x)^2 = (10/3)^2`
= `x^2 + 1/x^2 + 2 = 100/9`
= `x^2 + 1/x^2 = 100/9 - 2`
= `x^2 + 1/x^2 = (100 - 18)/9`
∴ `x^2 + 1/x^2 = 82/9`
Also,
`x - 1/x = sqrt((x + 1/x)^2 - 4)`
= `sqrt(100/9 - 4)`
= `sqrt(64/9)`
∴ `x - 1/x = 8/3`
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