Question

The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers . 

 

Answer 1

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.