Question 45868: Hi again,
I could use some assistance with this problem:
Prove that if the sum of two numbers is constant, then their product is maximum if the numbers are equal.
Thank you,
Louis
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Prove that if the sum of two numbers is constant, then their product is maximum if the numbers are equal.
1st: Let x+y = k, where k is some constant.
2nd: Then y=k-x
3rd: The product of x and y is xy=x(k-x)=kx-x^2
This is a quadratic with a=-1, b=k
The maximum value of this product occurs when x=-b/2a
x=-b/2a= -k/-2 = k/2
Substitute that into the 1st equation to get the following:
(k/2)+ y=k
y=k/2
So both x and y are k/2; therefore they are equal.
Cheers,
Stan H.
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