# The product of two consecutive odd integers is 99, how do you find the integers?

Feb 16, 2016

Consecutive integers are $- 11$ and $- 9$ or $9$ and $11$

#### Explanation:

Let the numbers be $\left(2 x - 1\right)$ and $\left(2 x + 1\right)$ as for any $x$ these will be consecutive odd numbers. Hence

$\left(2 x - 1\right) \left(2 x + 1\right) = 99$ i.e.

$4 {x}^{2} - 1 = 99$ or $4 {x}^{2} - 100 = 0$ or ${x}^{2} - 25 = 0$

i.e. $\left(x - 5\right) \left(x + 5\right) = 0$ i.e. $x = 5 \mathmr{and} - 5$

Hence consecutive integers are $- 11$ and $- 9$ or $9$ and $11$.