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What is the greatest product obtainable from two integers whose sum is \(24\)?

 May 25, 2022
 #1
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12  +  12 ==24

 

12  x  12 ==144

 May 25, 2022
 #2
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let x and y represent the two integers respectively. 

 

we know that their sum is 24. we could then isolate for one variable:

 

x + y = 24

      y = 24 - x

 

their product would then be: 

 

xy = x(24 - x)

     = 24x - x2 

     = -(x2 - 24x) 

     = -(x - 24x + 144 - 144) 

     = -[(x - 12)2 - 144]

     = -(x - 12)2 + 144

 

In vertex form, we can see the maximum. 

The answer is 144.

 May 25, 2022

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