SOLUTION: Find two positive numbers satisfying the given requirements. The product is 200 and the sum is a minimum.

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Question 1125299: Find two positive numbers satisfying the given requirements. The product is 200 and the sum is a minimum.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Both numbers, 10%2Asqrt%282%29.

system%28xy=200%2CA=x%2By%29

y=200%2Fx
-
A=x%2B200%2Fx
dA%2Fdx=1-200%2Fx%5E2
-
1-200%2Fx%5E2=0
%28x%5E2-200%29%2Fx%5E2=0
x%5E2-200=0
x%5E2=200
x=10%2Asqrt%282%29
-
y=200%2Fx
y=200%2F%2810%2Asqrt%282%29%29
.