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Question
The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.
Solution
Let one numbers be x then other (9 - x).
Then according to question
`1/x + 1(9-x)=1/2`
`rArr((9-x)+x)/(x(9-x))=1/2`
`rArr9/(x(9-x))=1/2`
By cross multiplication
⇒ 18 = x(9 - x)
⇒ x2 - 9x + 18 = 0
⇒ x2 - 6x - 3x + 18 = 0
⇒ x(x - 6) - 3(x - 6) = 0
⇒ (x - 6)(x - 3) = 0
⇒ x - 6 = 0
⇒ x = 6
Or
⇒ x - 3 = 0
⇒ x = 3
Since, x being a number,
Therefore,
When x = 6 then
(9 - x) = (9 - 6) = 3
When x = 3 then
(9 - x) = (9 - 3) = 6
Thus, two consecutive number be either 3, 6 or 6, 3.
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