Question

the product of two consecutive even integersis 34 less than 7 times their sum.find the two integers.

Answer 1

let the first integer be x
then the second even integer is x+2

x(x+2) = 7(x + x+2) - 34
x^2 + 2x = 14x + 14 - 34
x^2 - 12x + 20 = 0
(x-10)(x-2) = 0
x = 10 or x = 2

the numbers are 10 and 12 or the numbers are 2 and 4

check:
case 1: numbers are 10 and 12
product = 120
7 times their sum = 154
is 120 less than 154 by 34 ? YES

case 2: numbers are 2 and 4
product = 8
7 times their sum = 42
is 8 less than 42 by 34 ? YES!

So we have two answers:
the integers could be 10 and 12
or
the integers could be 2 and 4