Question

One positive integer is two less than twice the other. The product of the two is 84. Find the integers

Answer 1

`x=2y-2`

`xy=84`

Plug the first equation into the second to get


`(2y-2)y=2y^2-2y=84\implies 2y^2-2y-84=0\implies y^2-y-42=(y-7)(y+6)=0`

It's clear that both integers are positive, so it must be the case that
`y=7`, which means
`x=12`.