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Question
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
Solution
Let the required natural numbers be x and(9'-x).
According to the given condition,
`1/x+1/(9-x)=1/2`
⇒`(9-x+x)/(x(9-x))=/12`
⇒`9/(9x-x^2)=1/2`
⇒`9x-x^2=18`
⇒`x^2-9x+18=0`
⇒`x^2-6x-3x+18=0`
⇒`x(x-6)-3(x-6)=0`
⇒`x-3=0 or x-6=0`
⇒`x=3 or x=6`
When `x=3`
`9-x=9-3=6`
When` x=6`
`9-x=9-6=3`
Hence, the required natural numbers are 3 and 6.
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