## anonymous 5 years ago Among all pairs of numbers whose difference is 10, find a pair whose product is as small as possible. What is the minimum product? a. the pairs of numbers whose difference is 10 and whose product is as small as possible is___ b. The minimum product is___

1. anonymous

bet it is -5 and 5

2. anonymous

call one number x, the other x + 10 then their product is $x(x+10)=x^2+10x$

3. anonymous

this thing has a minimum value at $x=-\frac{b}{2a}=-\frac{10}{2}=-5$

4. anonymous

x = -5, x+10 = 5 and their product is -25