Among all pairs of numbers whose difference is 20, find a pair whose product is as small as possible. What is the minimum product? The pair of numbers whose difference is 20 and whose product is as small as possible is (Use a comma to separate answers.)

To minimize the product of the two numbers \( x \) and \( y \) where \( x - y = 20 \), we can express \( y \) in terms of \( x \): \( y = x - 20 \). Therefore, the product \( P \) becomes \( P = x \cdot (x - 20) = x^2 - 20x \). This quadratic opens upwards, so its minimum occurs at the vertex, given by \( x = \frac{-b}{2a} = \frac{20}{2} = 10 \). Hence, \( y = 10 - 20 = -10 \). The pair is (10, -10) and the minimum product is \( 10 \times -10 = -100 \). So, the pair of numbers whose difference is 20 and whose product is as small as possible is 10, -10. The minimum product is -100.