SOLUTION: Among all pairs of numbers whose sum is 26, find a pair whose product is as large as possible. What is the maximum product?

Algebra ->  Test  -> Lessons -> SOLUTION: Among all pairs of numbers whose sum is 26, find a pair whose product is as large as possible. What is the maximum product?      Log On


   

Question 472545: Among all pairs of numbers whose sum is 26, find a pair whose product is as large as possible. What is the maximum product?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
{13,13}, maximum product is 169. There are several ways to prove this.

Let a, 26-a be the two numbers, in which we want to maximize a(26-a). We can either use the fact that it is quadratic in terms of a and find the vertex, or use the AM-GM inequality. Both methods yield a = 13 maximizing the product.