Question

The product of two consecutive odd natural numbers is $99$. Find the numbers.

Answer 1

Let $x$ and $x+2$ be the two consecutive odd natural numbers.
$\begin{array}{cc}\left(x\right)\times (x+2)& =99\\ x^2+2x& =99\\ x^2+2x-99& =0\\ x^2+11x-9x-99& =0\\ x(x+11)-9(x+11)& =0\\ (x+11)(x-9)& =0\end{array}$

$\therefore$ $x=-11$ or $x=9$
But $x$ is a natural number, so it can not be negative hence, $x=-11$ is not a valid solution.

$x+2=11$
$\therefore$ The consecutive odd numbers are $9$ and $11.$