Find the greatest product of two numbers whose sum is 12
In order to find the greatest product of two numbers whose sum is 12, we need to find two numbers that are as close together as possible. This is because, according to the concept of arithmetic mean and geometric mean inequality, the product of two numbers is maximized when the two numbers are equal.
Two numbers whose sum is 12 and are as close together as possible would be 6 and 6.
Therefore, the greatest product of two numbers whose sum is 12 is 6 multiplied by 6, which equals 36.
To find the greatest product of two numbers whose sum is 12, we can use the concept of maximizing a product when we have a fixed sum.
Let's assume the two numbers are x and y, such that x + y = 12.
To maximize the product, we can consider finding the numbers that are closest to each other, as the product of two numbers becomes greater when they are closer together.
In this case, let's take x = 6 and y = 6. Their sum is indeed 12, and the product is x * y = 6 * 6 = 36.
Therefore, the greatest product of two numbers whose sum is 12 is 36.