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

Question

The difference of two natural numbers is 3 and the difference of their reciprocals is \(\frac{3}{28}.\) Find the numbers.

Answer 1

Let the natural numbers be ‘a’ and ‘b’. 

Given, difference of two natural numbers is 3 and difference of their reciprocals is 3/28 

⇒ a – b = 3 

⇒ a = b + 3 

and 1/b – 1/a 

= 3/28 

⇒ 1/b – 1/(b + 3) = 3/28 

⇒ 28(b – b – 3) = -3(b² + 3b) 

⇒ b² + 3b - 28 = 0 

⇒ b² + 7b – 4b – 28 = 0 

⇒ b(b + 7) – 4(b + 7) = 0 

⇒ (b – 4)(b + 7) = 0 

⇒ b = 4 

Numbers are, 4, 7