Determine two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Explanation

To solve the problem of finding two positive numbers whose sum is 15 and the sum of their squares 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
According to the problem, we have:
\[ x + y = 15 \]
...