Question

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

Answer 1

Let $x,y$ be the required natural numbers

$x-y=3$

$\frac{1}{y}-\frac{1}{x}=\frac{3}{28}$

$\frac{x-y}{xy}=\frac{3}{28}$

$xy=28$

For $(xy=28),(x,y)$ can be $(1,28)(2,14)(4,7)(28,1)(14,2)(7,4)$

Only $(x,y)=(7,4)$ stability $x-y=3$

$x=7,y=4$

$x+y=4+7=11$

Sum is $11$