The product of two consecutive positive integers is 72. Find the integers.
Let's call the smaller integer "x" and the larger integer "x+1" (since they are consecutive, the larger one will be one more than the smaller one).
According to the problem, the product of these two integers is 72. In other words:
x(x+1) = 72
Expanding the parentheses, we get:
x^2 + x = 72
Subtracting 72 from both sides, we get:
x^2 + x - 72 = 0
Now we have a quadratic equation, which we can solve using factoring or the quadratic formula. Let's try factoring first. We're looking for two numbers that multiply to -72 and add up to 1 (since the coefficient of the x term is 1). After some trial and error, we find that:
x = 8, x+1 = 9
When we plug these values back into the original equation, we can confirm that they work:
8(8+1) = 72
72 = 72
So the two consecutive positive integers that have a product of 72 are 8 and 9.