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Question
The sum of a number and its reciprocal is `2 9/40`. Find the number.
Solution
Let the number be A. Then as per the question,
`"A" + 1/ "A" = 2 9/40`
⇒ `"A"^2 + 1 - 89/40 "A" = 0`
⇒ 40 A2 + 40 - 89 A=0
⇒ 40A2 - 89A + 40 = 0
⇒ 40 A2 - 64A - 25A + 40 = 0
⇒ 8A (5A - 8) - 5 (5A-8) = 0
⇒ (8A - 5)(5A - 8) = 0
⇒ A = `5/8 , 8/5`
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