Question 1191565
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Let the two numbers whose sum is 12 be 6+x and 6-x; their product is then 36-x^2.<br>
x^2 is always 0 or positive, so the maximum value of 36-x^2 is when x^2 is 0, which means x is 0.<br>
The two positive numbers with a sum of 12 for which the product of the two numbers is maximum are then 6+0=6 and 6-0=6.<br>
ANSWER: 6 and 6<br>