Question

What is the pair of integers when the product is 20 and he sum is 9??

Answer 1

4, 5

Explanation:

Let our integers be `x` and `y`.

From the question:

`xy=20`
`x+y=9`

By rearranging the second equation:

`x=9-y`

Substitute this into the first equation:

`y(9-y)=20`
`9y-y^2=20`
`-y^2+9y-20`0# #y^2-9y+20=0# #(y-4)(y-5)=0#

`y=4` or `y=5`

Sub these into either of the two equations to find x:

Let `y=4`

`4x=20`
`x=5`

Let `y=5`
`5x=20`
`x=4`

So `x=4, y=5` or `x=5, y=4`

Either way, our two integers are `4` and `5`