Question

The sum of the reciprocals of two consecutive odd natural numbers is $\frac{12}{35}$. Find those numbers.

Answer 1

Let the numbers be $x$ and $x+2$

Thus,

$\frac{1}{x}+\frac{1}{(x+2)}=\frac{12}{35}$

$35(x+2)+35x=12x(x+2)$

$12x^2-46x+70=0$

$6x^2-23x+35=0$

$(6x+7)(x-5)=0$

$x=-\frac{7}{6}x=5$

Since $x$ is an integer so, $x=5$

Therefoe numbers are $5$ and $7$