# The product of two consecutive even integers is 1088. What are the numbers?

Jun 27, 2016

$\left\{- 34 , - 32\right\}$ or $\left\{32 , 34\right\}$

#### Explanation:

Let $n$ be the lesser of the two consecutive even integers. Then $n + 2$ is the greater, and

$n \left(n + 2\right) = 1088$

$\implies {n}^{2} + 2 n = 1088$

$\implies {n}^{2} + 2 n - 1088 = 0$

If we attempt to factor by grouping , we find

$\left(n - 32\right) \left(n + 34\right) = 0$

$\implies n - 32 = 0 \mathmr{and} n + 34 = 0$

$\implies n = 32 \mathmr{and} n = - 34$

Thus, we have two pairs of consecutive even integers which fulfill the criteria: $\left\{- 34 , - 32\right\}$ or $\left\{32 , 34\right\}$