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If the product of 2 numbers if 84 what is the minimum value of their sum.

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xetaalpha2 | Student | Honors

Posted March 24, 2012 at 3:31 PM via web

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If the product of 2 numbers if 84 what is the minimum value of their sum.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 24, 2012 at 3:46 PM (Answer #1)

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The product of two numbers is 84. If one of the numbers is x, the other number is `84/x` . It is possible to find a minimum value of the sum if the numbers are assumed to be positive.

S =` x + 84/x`

S' = `1 - 84/x^2`

`1 - 84/x^2 = 0`

=> `84/x^2 = 1`

=> `x^2 = 84`

=> x = `sqrt 84` and x = `-sqrt 84`

`S'' = 168/s^3`

S'' is positive for `x = sqrt 84`

This gives the minimum value of the sum of the two numbers that are assumed to be positive as `2*sqrt 84` .

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