Question

(BE)² = MPB, where B, E, M and P are distinct integers. Then M =

• A. 2
• B. 3
• C. 9
• D. None of these

Hint:

When working with distinct integer solutions, try different factorizations and check for consistency with the equation.

Answer 1

The Correct Option is B

We are given the equation: \[ (BE)^2 = MPB, \] where \( B, E, M, P \) are distinct integers. We need to determine the value of \( M \). Step 1: Express the equation clearly \[ (BE)^2 = MPB \quad \Rightarrow \quad B^2 E^2 = MPB. \] Step 2: Simplify the equation Now, divide both sides by \( B \) (assuming \( B \neq 0 \)): \[ B E^2 = MP. \] Step 3: Try different values for the distinct integers Since we know that \( B, E, M, P \) are distinct integers, let us try values for \( B \) and \( E \) that satisfy this equation. Let \( B = 1 \) and \( E = 3 \), then: \[ B E^2 = 1 \times 3^2 = 9, \] which means \( MP = 9 \). Now, since \( M \) and \( P \) are distinct integers, we can factor 9 as: \[ M = 3, \, P = 3. \] Thus, the value of \( M \) is \( 3 \).