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Question
If `x + 1/x = 2.5`, the value of x is ______.
Options
4
`5 and 1/5`
`2 or 1/2`
`2 and 1/2`
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Solution
If `x + 1/x = 2.5`, the value of x is `underlinebb(2 or 1/2)`.
Explanation:
Given `x + 1/x = 2.5 = 25/10 = 5/2`
`\implies (x^2 + 1)/x = 5/2`
`\implies` 2(x2 + 1) = 5x ...[Cross multiplying]
`\implies` 2x2 + 2 – 5x = 0
`\implies` 2x2 – 5x + 2 = 0
`\implies` 2x2 – 4x – x + 2 = 0
`\implies` 2x(x – 2) – 1(x – 2) = 0
`\implies` (x – 2)(2x – 1) = 0
Either x – 2 = 0 or 2x – 1 = 0
`\implies` x = 2 or x = `1/2`
`\implies` x = 2 or `1/2`
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