Question

one positive integer is 7 less than another. The product of two integers is 44. what are the integers?

Answer 1

The two integers are: 4 and 11.

Explanation:

We are given that one positive integer is 7 less than another. Given that the product of two integers is 44, we are to find the integers.

Assuming
`x` to be one positive integer and
`y` to be the other, we can write it as:

`x=y-7` --- (1)

`x.y=44` --- (2)

Substituting x from (1) in (2):

`(y-7).y=44`

`y^2-7y-44=0\\\\y^2-11y+4y-44=0\\\\y(y-11)+4(y-11)`

y = 11

Substituting y = 11 in (1) to find x:

`x=11-7`

x = 4

Answer 2

4 and 11

Explanation:

Lets call the smallest n

And the other one n+7

Then,

n.(n+7)=44

n²+7n=44

Subtract 44 from both sides.

n²+7n-44=44-44

n²+7n-44=0

Factorize the equation.

n²+11n-4n-44=0

n(n+11)-4(n+11)=0

(n+11)(n-4)=0

n+11=0 , n-4=0

n=-11 , n=4

n=4 is the only positive solution, so the numbers are:

4 and 11....