SOLUTION: Find two real numbers whose sum is 18 and whose product is a minimum?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find two real numbers whose sum is 18 and whose product is a minimum?      Log On


   

Question 357839: Find two real numbers whose sum is 18 and whose product is a minimum?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be X and Y.
X%2BY=18
Y=18-X
.
.
.
P=X%2AY=X%2A%2818-X%29=18X-X%5E2
To find the min or max of a quadratic, convert to vertex form.
P=-X%5E2%2B18X=-%28X%5E2-18X%29
P=-X%5E2%2B18X=-%28X%5E2-18X%2B81%29%2B81
P=-X%5E2%2B18X=-%28X-9%29%5E2%2B81
The min occurs at X=9 and equals
P%5Bmin%5D=81