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