What is the greatest product obtainable from two integers whose sum is \(24\)?
+592 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.
