Question

How do you determine three consecutive even integers such that the first times the third, is 4 less than 12 times the second?

Answer 1

-2,0,2
or 10,12,14

Explanation:

First of all, lets call the integers `(x-2),(x),(x+2)`. We can do this because consecutive integers differ by 2. Now from the information we have, we can make an equation:
`1st*3rd =12*2nd-4`
`(x-2)(x+2)=12*(x)-4`
`x^2-2x+2x-4=12x-4`
`x^2-4=12x-4`
`x^2=12x`
`x^2-12x=0`
`x(x-12)=0`
Now you see that there are two solutions to this, when `x=0` and `x=12`.
So our integers can be:
-2,0,2
or 10,12,14