The product of two consecutive even numbers is $3248$, what is the larger number? The product of two consecutive even numbers is $3248$. Actually, I am interested in finding the larger number out of the two.

Say one of the even numbers is $a$ and the consecutive even number is $a+2$, then
$a(a+2) = 3248$, so we can get the larger number by finding the roots of the above quadratic equation.

I was also thinking of another method of applying the product and the sum of the roots!. from which I conclude that one of the roots is negative and the other root is positive.

Any other method of obtaining the larger number without calculating the roots of the quadratic equation?
You can also take two consecutive numbers as $a-1$ and $a+1$ the we have:

$a^2-1=3248$

$a^2=3249$

etc...
let $x$ &amp; $x+2$ be $2$ consecutive even numbers
$$
\begin{align}
(x)(x+2)&amp;=3248 \\
x^2 + 2x -3248 &amp;= 0 \\
x^2 + 58x - 56x - 3248 &amp;= 0 \\
x(x + 58) - 56(x + 58) &amp;= 0 \\
(x - 56)(x + 58) &amp;= 0 \\
\end{align}
$$
$x = 56$ since the value could not be in negative.
$x + 2 = 58$ which is the largest number.