Question

Find two consecutive even integers such that the square of the first, decreased by the second is 130

Answer 1

Let's make the first even integer m and the second even integer n. The square of the first, decreased by the second is 130 is:

$m^{2}$-n=130  ---> Add n to each side
$m^{2}$=130+n ---> Take the square root of each side
m=±$\sqrt{130+n}$

Let's look at the first square number above 130, which is $12^{2}$. m is 12, therefore the next consecutive even integer is 14.

$12^{2}$=144
144-14=130

The two consecutive integers are 12 and 14