## Pages

### Word problems on Quadratic Equations (6)

#### Question

Let there be two positive even integers such that the difference between them is 4. If their product is 96, find the numbers.

#### Solution :

Let the one even integer = x
The other even integer = x + 4

#### Given :

The product of integers = 96
Therefore,
(x)(x + 4) = 96
x^2 + 4x = 96
x^2 + 4x - 96 = 0
Splitting the middle term,
x^2 + 12x - 8x - 96 = 0
Factoring out x + 12,
x(x + 12) -8(x + 12) = 0
(x + 12) (x - 8) = 0
By zero product rule,
x + 12 = 0 or x - 8 = 0
x = -12 x = 8
x = {-12 , 8}
Answer is x = 8 and x + 4 = 12, so the two positive even integers are 8 and 12.