Explanation:

- We want to find the minimum value of \( x + y \) where \( xy = 4225 \).

- Start by finding factor pairs of 4225. The prime factorization of 4225 is \( 5^2 \times 13^2 \), which suggests pairs like \( (5^2, 13^2) \) or \( (5 \times 13, 5 \times 13) \).

- The pair \( x = 65 \) and \( y = 65 \) gives us \( x + y = 130 \).

- Other pairs include \( (25, 169) \) with \( x + y = 194 \); \( (1, 4225) \) with \( x + y = 4226 \); and so on.

- The smallest sum \( x + y = 130 \) is obtained with the pair \( (65, 65) \).

- Among the given options, the correct answer is:

- Option 1: 130