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Question
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
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Solution
Let one of the number be x then other number is (18 - x).
Then according to question,
`1/x+1/(18-x)=1/4`
`rArr(18 - x+x)/(x(18-x))=1/4`
⇒ 18 x 4 = 18x - x2
⇒ 72 = 18x - x2
⇒ x2 - 18x + 72 = 0
⇒ x2 -12x - 6x + 72 = 0
⇒ x(x - 12) - 6(x - 12) = 0
⇒ (x - 6)(x - 12) = 0
⇒ x - 6 = 0
⇒ x = 6
Or
⇒ x - 12 = 0
⇒ x = 12
Since, x being a number,
Therefore,
When x = 12 then another number will be
18 - x = 18 - 12 = 6
And when x = 6 then another number will be
18 - x = 18 - 6 = 12
Thus, the two numbers are 6 and 12.
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