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Find two positive numbers that satisfy the given requirements. (Enter youranswers as a comma-separated list.
The product is 186 and the sum is a minimum.

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To minimize the sum of two positive numbers while keeping their product constant at 186, we can use a bit of algebra. Let’s denote the two numbers as and . We have:

Using the first equation, we can express in terms of : . Now we can substitute this into the sum:

To find the minimum value, we can take the derivative of with respect to , set it to zero, and solve for . After doing the math, you’ll find the numbers are approximately 12 and 15.5 (the exact values are each), which gives the minimum sum while maintaining the required product!