What is the maximum possible product that can be attained by two numbers with a sum of −8?
-4 * -4 = 16
To find the maximum possible product of two numbers with a sum of -8, we need to understand the concept of optimization. In this case, we want to maximize the product, which means we need to find the two numbers that are as far apart as possible while still summing to -8.
Let's assume the two numbers are x and y, and their sum is -8. Mathematically, we can represent this as x + y = -8. To maximize the product, we need to maximize the difference between x and y.
To find the maximum possible product, we can use the concept of symmetry. Since the sum of x and y is -8, and we want to maximize the product, we want x and y to be as close as possible to 0. This symmetry means that the maximum product will be attained when x is half of -8 and y is also half of -8, i.e., x = -4 and y = -4.
Now, we can calculate the product of x and y: (-4) * (-4) = 16.
Therefore, the maximum possible product that can be attained by two numbers with a sum of -8 is 16.