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Question
If the difference between a number and its reciprocal is `24/5`, find the number
Solution
Let the number be “x” and its reciprocal is `1/x`
By the given condition
`x - 1/x = 24/5`
`(x^2 - 1)/x = 24/5`
5x2 – 5 = 24x
5x2 – 24x – 5 = 0
5x2 – 25x + x – 5 = 0
⇒ 5x(x – 5) + 1(x – 5) = 0
(x – 5) (5x – 1) = 0
⇒ x – 5 = 0 or 5x + 1 = 0
x = 5 or 5x = – 1
⇒ x = `(-1)/5`
The number is 5 or `(-1)/5`
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