Question

If ab = 1, bc = –9, c = –b and c < –a, what is the value of a + b? Express your

answer as a mixed number.

Answer 1

[AI-generated answer — Bot GPT 3.5]

We have c = -b and c < -a, which means -b < -a. Dividing both sides by -1, we get b > a. Since ab = 1, we know that a and b must be reciprocals.

From bc = -9, we substitute c = -b to get b(-b) = -9. Simplifying, we have b² = -9. Since b is positive (b > a), we take the positive square root of -9 to get b = 3.

Since a and b are reciprocals, we have a = 1/3. Therefore, a + b = 1/3 + 3 = 1/3 + 9/3 = 10/3.

So, the value of a + b is 10/3.