Find two positive numbers whose product is 81 and whose sum is a minimum. (if both values are the same number, enter it into both blanks.)

The two positive numbers will be 9 and 9.

Step-by-step explanation:

Let the two positive numbers be x and y.

It is given that the product of the number is 81 the sum of them is minimum.

So, the product can be written as .

The sum can be written as . It is required to minimize the sum.

Differentiate the sum as,

Now, the second derivative of the sum will be,

So, the second derivative is positive and hence, the sum will be minimum at x=9.

Therefore, the two positive numbers will be 9 and 9.

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The two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.

Step-by-step explanation:

81 is divisible by 1 and 81, since 81/1 = 81 and 81/81 = 1.

81 is divisible by 3 and 27, since 81/3 = 27 and 81/27 = 3.

81 is divisible by 9, since 81/9 = 9.

Their sums are.

81 + 1 = 82.

3 + 27 = 30

9 + 9 = 18.

So the two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.

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