Final answer:
To find the two consecutive positive even numbers whose product is 168, we can write and solve an algebraic equation.
Step-by-step explanation:
To find the two consecutive positive even numbers whose product is 168, we can use algebraic equations.
Let's call the first even number x. The next even number will be x + 2.
We can write the equation: x(x + 2) = 168.
Expanding the equation, we get: x^2 + 2x = 168.
Rearranging the equation, we get: x^2 + 2x - 168 = 0.
Now we can solve this quadratic equation by factoring or using the quadratic formula. By factoring, we find x = 12 or x = -14 (but we're looking for positive even numbers, so we discard the negative solution).
Therefore, the two consecutive positive even numbers whose product is 168 are 12 and 14.
Factoring the quadratic, we find that (x - 12)(x + 14) = 0. Thus, x = 12 or x = -14. However, we ignore x = -14 since we are looking for positive numbers. Therefore, the two consecutive positive even numbers are 12 and 14, which indeed have a product of 168.