Question

The sum of two natural numbers is 15 and the sum of their reciprocals is $\frac{3}{10}$. Find the numbers.

Answer 1

Sol:
Let one of the numbers be x.
Other number is (15 - x)
Sum of their reciprocals = 3/10
$1/x+1/(15-x)=3/10$
$\left(15\right)/(15x-x^2)=3/10$
$150=45x-3x^2$
$3x^2-45x+150=0$
$x^2-15x+50=0$
$(x-10)(x-5)=0$
$x=10or5$

Therefore, the numbers are 10 and 5.
If $x=15$