The difference of the squares of two positive consecutive even integers is 68 Find the integers Use the fact that, if x represents an even integer then x + 2 represents

the next consecutive even integer

Answer:different of two squares states that

If a²-b² is given then

a²-b² = (a+b) (a-b)

Now to answer the question

(x+2) ² - (x) ²=68

(x+2+x) ((x+2) - x) = 68

(2x+2) (x+2-x) = 68

(2x+2) (2) = 68

Divide both sides by 2

{ (2x+2) (2) }: 2 = 68/2

2x+2 = 34

Collect like terms

2x=34-2

2x=32

Divide both sides by 2

2x/2 = 32/2

x=16

Hence

x=16

x+2=16+2=18

The two consecutive even integer are 16 and 18