SOLUTION: Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.

Question 366968: Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.
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1st: x
2nd: y
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Equation:
x^2+y = 54
y = 54-x^2
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Product = x(54-x)^2 = 54x-x^3
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dP/dx = 54-3x^2
Solve: 54-3x^2 = 0
3x^2=54
x^2 = 18
x = sqrt(18)
y = 54-(sqrt(18))^2 = 36
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Cheers,
Stan H.
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