Question

The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers. 

 

Answer 1

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.