Is ab positive? 1. \((a+b)^2 < (a-b)^2\) 2. \(a = b\)

Explanation: The question asks: Is \(ab > 0\)? (Is \(ab\) positive?). **Statement 1:** \((a+b)^2 < (a-b)^2\). Expand both sides: \(a^2 + 2ab + b^2 < a^2 - 2ab + b^2\). Subtract \(a^2\) and \(b^2\) from both sides: \(2ab < -2ab\). Add \(2ab\) to both sides: \(4ab < 0\). Divide by 4 (a positive constant): \(ab < 0\). This definitively answers the question as NO, \(ab\) is not positive (it's negative). **Sufficient.**. **Statement 2:** \(a = b\). Case 1: If \(a = b = 1\), then \(ab = 1 \times 1 = 1\). Yes, \(ab\) is positive. Case 2: If \(a = b = 0\), then \(ab = 0 \times 0 = 0\). No, \(ab\) is not positive (it's zero). **Not Sufficient.**. Therefore, Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.