Question

The product of two consecutive positive odd numbers is 195. Find the numbers.

Answer 1

Step 1 : Framing the equation
Let one of the odd positive number be x. The other odd positive number will be (x + 2)
The product of the numbers is $x(x+2)=195\therefore x^2+2x-195=0$
Step 2: Solving the equation
$x^2+2x-195=0$
$x^2+15x-13x-195=0\therefore (x+15)(x-13)=0$
$x+15=0$ or $x-13=0\therefore x=-15$ or $x=13$
Step 3: Interpreting and finding the solution
Since the numbers must be positive, x = -15 is not taken.
$\therefore x=13$ and $x+2=13+2=15$
$\therefore$ The two consecutive odd positive numbers are 13 and 15.