Question

The difference of the squares of two positive consecutive even integers is 44 find the integers use the fact that if X represents an even integer then X +2 represents the next consecutive even integers

Answer 1

The 2 integers are 10 and 12

Explanation:

Translate it into english

"The difference (some subtraction) of the squares of two positive consecutive integers (
`x^2` and
`(x+2)^2`) is (=) 44 (44)"

this means the following:

`(x+2)^2-x^2=44`

solve for x to find the smaller integer

first, expand

`(x^2+4x+4)-x^2=44`

`x^2+4x+4-x^2=44`

`4x+4=44`

`4x=40`

`x=10\rightarrow x+2=10+2=12`

The 2 integers are 10 and 12