SOLUTION: please help me to solve this problem. "Find two real numbers whose sum is 18 and whose product is a minimum." tnx

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Question 348454: please help me to solve this problem. "Find two real numbers whose sum is 18 and whose product is a minimum." tnx
Found 2 solutions by Fombitz, hairejem@gmail.com:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%2BB=18
THe product is,
P=A%2AB
SUbsitute from above,
A=18-B
P=%2818-B%29B=18B-B%5E2
To find the maximum, convert to vertex form, y=a%28x-h%29%5E2%2Bk, since the maximum occures at the vertex (h,k).
Complete the square to convert to vertex form,
P=-%28B%5E2-18B%29
P=-%28B%5E2-18B%2B81%29%2B81
P=-%28B-9%29%5E2%2B81
The maximum occurs at B=9, when A=9, and P=81.

Answer by hairejem@gmail.com(1) About Me  (Show Source):
You can put this solution on YOUR website!
When you want to find the MAXIMUM product from two real numbers whose sum is 18, the answer is 81. But if you want to find the MINIMUM product of two real numbers whose sum is 18, there is a problem because if your two real numbers are 0 and 18, the product is 0. But it is not yet the minimum because there are still pairs of real numbers with a sum of 18 that gives lesser products. For example, -1 and 19 whose product is -19, -2 and 20 whose product is -40, and so on...