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Question
The sum of a number and its reciprocal is 4.25. Find the number.
Solution
Let the numbers be x and `1/x`
Form the given information,
`x + 1/x = 4.25`
`(x^2 + 1)/x = 425/100 = 17/4`
4x2 – 17x + 4 = 0
4x2 – 16x – x + 4 = 0
4x(x – 4) – 1(x – 4) = 0
(x – 4)(4x – 1) = 0
`x = 4,1/4`
`x = 4 => 1/x = 1/4`
`x = 1/4 => x = 4`
Thus, the number are 4 and `1/4`
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