The difference of the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

Explanation

To solve the problem step by step, we will define the two numbers and set up equations based on the conditions given in the question.

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

### Step 2: Set Up the Equations
From the problem statement, we have two conditions:
1. The difference of the squares of the two numbers is 45:
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