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

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Answer 1 · 2016-06-27T01:13:20

${- 34, - 32}$ ${-34, -32}$ or ${32, 34}$ ${32, 34}$

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

$n (n + 2) = 1088$ $n(n+2) = 1088$

$\Rightarrow n^{2} + 2 n = 1088$ $=> n^2+2n = 1088$

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

If we attempt to factor by grouping , we find

$(n - 32) (n + 34) = 0$ $(n-32)(n+34) = 0$

$\Rightarrow n - 32 = 0 or n + 34 = 0$ $=> n-32 = 0 or n+34 = 0$

$\Rightarrow n = 32 or n = - 34$ $=> n = 32 or n = -34$

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