Question

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 1

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

Explanation: