Question

The product of two consecutive positive integers is 72. Find the integers.

Answer 1

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.