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 find the pair of numbers whose difference is 20 and yields the minimum product, we can represent the numbers as \( x \) and \( y = x - 20 \). The product \( P \) of these two numbers is given by \( P = x(x - 20) = x^2 - 20x \). This is a quadratic equation that opens upwards, indicating that it has a minimum point. The vertex of the parabola occurs at \( x = -\frac{b}{2a} = \frac{20}{2} = 10 \). Therefore, the values of \( x \) and \( y \) are \( 10 \) and \( -10 \). Thus, the pair of numbers whose difference is 20 and whose product is as small as possible is \( (10, -10) \) and the minimum product is \( -100 \). 10, -10