Question

The product of two consecutive odd integers is equal to $675$. Find the two integers.

Answer 1

Let us take the first number as $x$ and the second number as $x+2$ now we get the equation as
$x\times (x+2)=675$
$x^2+2x=675$
Here to make both the sides a perfect square we add 1 to both the sides and get,
$x^2+2x+1=675+1$
${(x+1)}^2=676$
$x+1=\sqrt{676}$
$x+1=26$
$x=26-1$
$x=25$
So the two consecutive numbers are
$x=25$ and
$x+2=27$
As the product of the two numbers is 675 both these numbers can either be positive or negative.
Ans: 25 and 27
or -25 and -27