#### 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.

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