Question

The product of two consecutive even integers is 440, find the integers...

Answer 1

Bear in mind that, if you multiply any integer, by 2,  you always get an EVEN number, no matter whatsoever what that integer is.  Say 2*2 = even, 17*2= even, 37*2 = even and so on.

So, let's pick a reference integer, say "a", so, 2 * a, we know is an EVEN integer, so our first integer is 2a then.

Now, to get a consecutive integer from any even integer, all you do is, hop backwards one spot, or forwards one spot, like say, 2 + 2, or 2-2, or  6 + 2, or 6 -2 and so on.

Therefore, since our first even integer is 2a, then the next one can just be say, 2a + 2.

Now, we know their product is 440, thus

$\bf (2a)(2a+2)=440\implies 4a^2+4a=440\implies 4(a^2+a)=440 \\\\\\ a^2+a=110\implies a^2+a-110=0\implies (a+11)(a-10)=0 \\\\\\ a= \begin{cases} -11\\ \boxed{10} \end{cases}$

so.. recall that "a" was only our reference integer, so the even number integers are then 2a and 2a + 2, or 2(10)  and 2(10) + 2.