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Question
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
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Solution
Let the required natural numbers be x and (x+3)
Now,` x<x+3`
∴`1/x>1/(x+3)`
According to the given condition,
`1/x-1/(x+3)=3/28`
⇒`(x+3-x)/(x(x+3))=3/28`
⇒`3/(x^2+3x)=3/28`
⇒ `x^2+3x=28`
⇒`x^2+3x-28=0`
⇒`x^2+7x-4x-28=0`
⇒`x(x+7)-4(x+7)=0`
⇒`(x+7)(x-4)=0`
⇒`x+7=0 or x-4=0`
⇒`x=-7 or x=4`
∴ `x=4` ( -7 is not a natural number)
When `x=4`
`x+3=4+3=7`
Hence, the required natural numbers are 4 and 7.
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