Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

Explanation

To find two positive numbers whose sum is 16 and the sum of whose cubes is minimized, we can follow these steps:

### Step 1: Define the Variables
Let the two positive numbers be \( x \) and \( y \).

### Step 2: Set Up the Equation for the Sum
According to the problem, the sum of the two numbers is given by:
\[
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