Question 1179580
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To get a sum of 16, let the two numbers be 8-a and 8+a, where a is constant.<br>
The sum of the two numbers is 16; and the product is (8-a)(8+a)=64-a^2.<br>
The maximum value of 64-a^2 is when a=0, because a^2 is always non-negative.<br>
So the maximum value of the product is when a=0, making the two numbers 8-0=8 and 8+0=8.<br>
ANSWER: 8 and 8<br>
Note there is nothing special about the number 16 as the sum of the two numbers.  It is always true that for a given sum of two numbers, the maximum product of the two numbers is when they are equal.<br>