Question

The product of two consecutive even positive integers is 674 more than the sum of the two integers. Find the integers.

Answer 1

$2n(2n+2)=2n+2n+2+674\\ 4n^2+4n=4n+676\\ 4n^2=676\\ n^2=169\\ n=-13 \vee n=13$
$-13\not\ \textgreater \ 0$

$n=13\\ 2n=26\\ 2n+2=28$

It's 26 and 28.