Question

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

Answer 1

There are some mistake in question according to me there are difference of two natural number is 3 which solution given below.

Let the nos be X and X+3.
Their reciprocals are
$1/x$ and $1/x+3$

Now $1/x-1/x-3=3/28$

So, $x+3-x/x^2+3x=3/283\ast 28=3x^2+9x84=3x^2+9x3x^2+9x-84=0/3x^2+3x-28=0(x+7)(x-4)=0$
Now
$x=-7$ or $x=+4$
Case-1
$x=-7x+3=-7+3=-4$
Now
$-4-(-7)=-4+7=+3$.
Case-2
$x=+4x+3=4+3=7$
Now
$7-4=+3$
Therefore the nos are 7 and 4.