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

Answer:

The 2 integers are 10 and 12

Step-by-step 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