Find two positive numbers whose sum is 14 and the sum of whose squares is minimum.

Explanation

To solve the problem of finding two positive numbers whose sum is 14 and the sum of whose 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 for the Sum
According to the problem, the sum of the two numbers is:
\[
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