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

Answer:

$11, 5$

Step-by-step 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.

$x=y-6$

$x=11-6$

$x=5$

Answer 2

Answer:

5, 11.

Step-by-step 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.