What is the minimum sum of the numbers if the product of 2 numbers is 81?
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The product of two numbers is 81. If one of the numbers is 81, the other number is 81/x.
The sum of the numbers is S = x + 81/x. To find the minimum value of S, S' = 0 has to be solved for x.
S' = 1 - 81/x^2
1 - 81/x^2 = 0
=> x^2 = 81
=> x = 9 and x = -9
An assumption has to be made that the numbers are positive to be able to determine the minimum sum.
The minimum sum of the numbers is 18.
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