# Among all pairs of numbers whose sum is 100, how do you find a pair whose product is as large as possible. (Hint: express the product as a function of x)?

##### 1 Answer

#### Explanation:

Suppose two numbers sum to equal

As

To put it into vertex form, we use a process called completing the square:

#=-(x^2-100x)-(100/2)^2+(100/2)^2#

#=-(x^2-100x)-2500+2500#

#=-(x^2-100x+2500)+2500#

#=-(x-50)^2+2500#

Thus the vertex is at

As such, the pair of numbers