Đặt P = A.B, tìm các giá trị của x nguyên để P < 1. Tìm số nguyên x để P có giá trị là số nguyên

To solve the given problem where \( P = A \cdot B \), let's address each part step by step.

### b) Find integer values of \( x \) such that \( P < 1 \)

1. Since \( P = A \cdot B \), we need to have \( A \cdot B < 1 \).
2. This implies that one of the following must be true:
- \( A < 1 \) and \( B > 1 \) (or vice versa).
3. Depending on the definitions of \( A \) and \( B \) using \( x \), solve for \( x \).

### c) Find integer \( x \) such that \( P \) is an integer

1. For \( P = A \cdot B \) to be an integer, both \( A \) and \( B \) must be set up so the product is an integer.
2. Analyze \( A \) and \( B \) as functions of \( x \) and determine conditions under which \( P \) is integral.

### d) Find integers \( x \) such that \( P \) is an integer.

1. This will often overlap with the previous part, ensuring that conditions yield integer results.

### e) Find the minimum value of the expression

The expression \( Q = \frac{x + 4}{\sqrt{x - 1}} \) can be minimized as follows:

1. Identify the domain of \( Q \) (where \( x - 1 > 0 \) or \( x > 1 \)).
2. Utilize calculus or other analytical methods (like completing the square) to find critical points and determine minima.

By systematically analyzing the above components with the defined equations for \( A \) and \( B \) based on \( x \), you can reach the solutions for each part. Please provide any specific definitions or constraints for \( A \) and \( B \) if available for more precise calculation.