Question

If $|\square + 1| + (\square + 2)^2 = 0$ and $\square\square - 3\square\square = 1$, then the value of $\square$ is:

• A. \(1\)
• B. \( \frac{1}{2} \)
• C. \(5\)
• D. \(2\)

Hint:

Check all conditions and constraints carefully when dealing with absolute values and square terms. Ensure that all equations satisfy the conditions.

Answer 1

The Correct Option is A

Step 1: From the first equation, \( |a + 1| + (a + 2)^2 = 0 \), we know that for the sum to be zero, both terms must individually be zero. \[ |a + 1| = 0 \quad \Rightarrow \quad a = -1. \] Substituting \( a = -1 \) in the second equation \( a^2 - 3a = 1 \): \[ (-1)^2 - 3(-1) = 1 \quad \Rightarrow \quad 1 + 3 = 1, \] which is incorrect. Therefore, we check the second case for the second equation. The correct value of \( a \) is \(1\).