SOLUTION: What is the minimum product of two numbers whose difference is 32​? What are the​ numbers?

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Question 1090161: What is the minimum product of two numbers whose difference is 32​? What are the​ numbers?
Found 2 solutions by htmentor, Fombitz:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be x and y.
Their difference is 32, so y - x = 32 -> y = 32 + x
We want to minimize the product xy:
P = xy = x(32+x) = x^2 + 32x
P will be a minimum when the derivative is equal to zero.
dP/dx = 0 = 2x + 32, or x = -16
Thus y = 32 - 16 = 16
So the two numbers are 16 and -16 and the minimum product is -16*16 = -256

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y-x=32
y=x%2B32
So then,
xy=x%28x%2B32%29
xy=x%5E2%2B32x
Complete the square,
xy=%28x%5E2%2B32x%2B256%29-256
xy=%28x%2B16%29%5E2-256
So the minimum occurs when x=-16 and is equal to -256 so y=16