Question

The product of two consecutive even integers is 34 less than 7 times their sum, how do you find the two integers?

Answer 1

Let's call the numbers `2nand2n+2` with `n` an integer, and the `2` to make sure it's even.

Explanation:

Then we translate the rest of the conditions:
Product: `P=2n*(2n+2)=4n^2+4n`
Sum: `S=2n+(2n+2)=4n+2`

Now `P=7*S-34`

Substituting:
`4n^2+4n=7*(4n+2)-34->`
`4n^2+4n=28n+14-34->`

Everything to one side:
`4n^2-24n+20=0->`

Divide everything by `4` to make life easier:
`n^2-6n+5=0->` factorise:
`(n-1)(n-5)=0->n=1orn=5`

So the numbers are `2and4` or `10and 12`

Checking:
`2*4=7*(2+4)-34->8=42-34` check!
`10*12=7*(10+12)-34->120=154-34` check!