Question
When is 1/ab positive?
Answers
GPT-4o mini
The expression \( \frac{1}{ab} \) is positive when the product \( ab \) is also positive. This occurs in two scenarios:
1. Both \( a \) and \( b \) are positive. For example, if \( a = 2 \) and \( b = 3 \), then \( ab = 6 \), which is positive.
2. Both \( a \) and \( b \) are negative. For example, if \( a = -2 \) and \( b = -3 \), then \( ab = 6 \), which is also positive.
In summary, \( \frac{1}{ab} \) is positive when:
- \( a > 0 \) and \( b > 0 \), or
- \( a < 0 \) and \( b < 0 \).
1. Both \( a \) and \( b \) are positive. For example, if \( a = 2 \) and \( b = 3 \), then \( ab = 6 \), which is positive.
2. Both \( a \) and \( b \) are negative. For example, if \( a = -2 \) and \( b = -3 \), then \( ab = 6 \), which is also positive.
In summary, \( \frac{1}{ab} \) is positive when:
- \( a > 0 \) and \( b > 0 \), or
- \( a < 0 \) and \( b < 0 \).