Question

One positive integer is 6 less than another. The

product of the two integers is 55. What are the
integers?
Separate the answers with a comma.

Answer 1

5, 11.

Explanation:

If the larger integer is x then the smaller one is x - 6.

Also x(x - 6) = 55

x^2 - 6x = 55

x^2 - 6x - 55 = 0

(x - 11)(x + 5) = 0

x = 11, -5.

We are given that x is positive so its value is 11.

The 2 integers are 5 and 11.

Answer 2

`11, 5`

Explanation:

`x=y-6`

`xy=55`

Put x as y-6 in the second equation.

`(y-6)y=55`

`y^2-6y=55`

`y^2-6y-55=0`

Factor.

`\left(y+5\right)\left(y-11\right)=0`

`\left(y+5\right)=0`

`y=-5`

It has to be a positive integer.

`y-11=0`

`y=11`

Substitute y as 11.

`x=y-6`

`x=11-6`

`x=5`