Question

The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers 

Answer 1

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.