Question

The difference of the squares of two positive consecutive even integers is 92. find the integers.

Answer 1

consecutive even integers are 2 apart
they are x and x+2

differnce between the squares

$(x+2)^2-(x)^2=92$
expand
$x^2+4x+4-x^2=92$
$4x+4=92$
minus 4 both sides
$4x=88$
divide both sides by 4
$x=22$
$x+2=24$
the integers are 22 and 24

Answer 2

The two integers are 22 and 24 if the difference of the squares of two positive consecutive even integers is 92.

What is a number system?

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Let's say the first even integer is x then the second even will be x + 2(for example if 4 is even then 4+2 = 6 will next even so)

Given,

The difference between the squares of two positive consecutive even integers is 92.

So,

(x+2)² - x² = 92

x² + 4x + 4 - x² = 92

4x + 4 = 92

4x = 88

x = 22

So, the next integer will be x + 2 i. e. 22 + 2 = 24

Hence "The two integers are 22 and 24 if the difference of the squares of two positive consecutive even integers is 92".

For more about the number system,

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