# How do you find two consecutive integers whose product is 72?

Nov 14, 2016

The two consecutive integers are
either
$\textcolor{w h i t e}{\text{XXX}} - 9 \mathmr{and} - 8$
or
$\textcolor{w h i t e}{\text{XXX}} 8 \mathmr{and} 9$

#### Explanation:

Let the smaller integer be $n$
$\rightarrow$ the larger integer will be $\left(n + 1\right)$

We are told
$\textcolor{w h i t e}{\text{XXX}} n \times \left(n + 1\right) = 72$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {n}^{2} + n - 72 = 0$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow \left(n + 9\right) \left(n - 8\right) = 0$

$\textcolor{w h i t e}{\text{XXX")n=-9color(white)("XX")orcolor(white)("XX}} n = 8$