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Question
The sum of a number and its reciprocal is `2 1/20` The number is
(a) `5/4 or 4/5` (b)`4/3 or 3/4`
(c) `5/6 or 6/5` (d) `1/6 or 6`
Solution
(a)` 5/4 or 4/5`
Let the required number be x.
According to the question
`x+1/x=41/20`
⇒`(x^2+1)/x=41/20`
⇒`20x^2-41x+20=0`
⇒`20x^2-25x-16x+20=0`
⇒`5x(4x-5)-4(4x-5)=0`
⇒`(4x-5) (5x-4)=0`
⇒`x=5/4 or x=4/5`
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