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What is the minimum sum of the numbers if the product of 2 numbers is 81?

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b52 | Student, Grade 9 | eNoter

Posted August 29, 2012 at 5:00 PM via web

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What is the minimum sum of the numbers if the product of 2 numbers is 81?

Tagged with calculus, math, minimum value

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 29, 2012 at 5:09 PM (Answer #1)

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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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