Final answer:
To find a pair of numbers where one number is 8 less than the other and their product is as small as possible, we can use algebra. The smallest possible product is 16.
Step-by-step explanation:
To find a pair of numbers where one number is 8 less than the other and their product is as small as possible, we can use algebra. Let's assume the first number is x. The second number would then be x + 8, since it is 8 more than the first number. The product of these two numbers would be x * (x + 8). To find the smallest possible product, we need to find the minimum of this quadratic equation. We can do this by finding the vertex, which is the lowest point of the parabola represented by the equation. The x-coordinate of the vertex is given by the formula -b/2a, where a is the coefficient of x^2, and b is the coefficient of x. In this case, the x-coordinate of the vertex would be (-8) / (2*1) = -4. Substituting this value back into the equation, we find that the smallest product is (-4) * (-4+8) = 16.