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Question
The sum of a number and its reciprocal is 4.25; the number is ______.
Options
`2 or 1/2`
`4 or 1/4`
`1/5 or 5`
`1/3 or 3`
Solution
The sum of a number and its reciprocal is 4.25; the number is `underlinebb(4 or 1/4)`.
Explanation:
Let the number be x
Then `x + 1/x = 4.25 = 425/100 = 17/4`
`\implies (x^2 + 1)/x = 17/4`
`\implies` 4(x2 + 1) = 17x
`\implies` 4x2 + 4 – 17x = 0
`\implies` 4x2 – 16x – x + 4 = 0
`\implies` 4x(x – 4) – 1(x – 4) = 0
`\implies` (x – 4)(4x – 1) = 0
Either x – 4 = 0 or 4x – 1 = 0
`\implies x = 4` or `x = 1/4`
`\implies x = 4` or `1/4`
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