Question

Find two numbers whose difference is 98 and whose product is a minimum. Step 1 If two numbers have a difference of 98 and we let x represent the smaller of these two numbers, then the larger of these two numbers is given by the following. _______

Answer 1

The two numbers whose difference is 98 and whose product is a minimum are -49 and 49. Algebraically, if x is the smaller number, then the larger number would be x + 98. To minimize the product x(x + 98), we find that the numbers are symmetric around the value zero.

Step-by-step explanation:

To find two numbers whose difference is 98 and whose product is a minimum, we can represent this problem algebraically. Let's assume x is the smaller number. Then the larger number would be x + 98. The product of the two numbers is x(x + 98). To find the minimum product, we can calculate this expression's derivative and find its critical points, or recognize that the product of two numbers with a fixed sum is minimized when the numbers are as close to each other as possible. This means the two numbers are 49 units away from the midpoint of the two numbers. Therefore, if x is the smaller number, x + 98 is the larger one, and the midpoint is x + 49. To minimize the product, we set x + 49 to zero and solve for x, which gives us x = -49 and the larger number as 49. This results in the numbers being -49 and 49, whose product is a minimum.

Answer 2

= 98-x.

Step-by-step explanation:

We're looking for the larger number. The small number is x and the difference btwn the numbers is 98. So the equation in the blank would be:

= 98-x.