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Question
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
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Solution
Let the required natural numbers be x and (x+5).
Now,`x<x+5`
∴ `1/x>1/(x+5)`
According to the given condition,
`1/x-1/(x+5)=5/14`
⇒`(x+5-x)/(x(x+5))=5/14`
⇒`5/(x^2+5x)=5/14`
⇒`x^2+5x-14=0`
⇒`x^2+7x-2x-14=0`
⇒`x(x+7)-2(x+7)=0`
⇒`(x+7)(x-2)=0`
⇒`x+7=0 or x-2=0`
⇒ `x=-7 or x=2`
∴x=2 ( -7 is not a natural number)
When x=2,
`x+5=2+5=7`
Hence, the required natural numbers are 2 and 7.
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