The product of two consecutive positive even integers is 48. Find the integers.
To find the consecutive positive even integers, we need to set up an equation based on the problem.
Let's assume the first even integer is x. Since the integers are consecutive, the second even integer would be x + 2.
According to the problem, the product of these two integers is 48, so we can write the equation:
x * (x + 2) = 48
To solve this quadratic equation, we can expand the equation:
x² + 2x = 48
Rearranging the equation:
x² + 2x - 48 = 0
Next, we need to factorize the quadratic equation:
(x + 8)(x - 6) = 0
Setting each factor equal to zero:
x + 8 = 0 or x - 6 = 0
Solving for x:
x = -8 or x = 6
Since we are looking for positive integers, we can disregard the negative solution. Therefore, the first even integer is x = 6.
To find the second even integer, we add 2 to the first integer:
Second integer = 6 + 2 = 8
So, the two consecutive positive even integers that have a product of 48 are 6 and 8.