Question

If a – b = 2 and ab = 3, find the value of a + b.

Answer 1

Given: a – b = 2 and ab = 3

Step-wise calculation:

1. We want to find (a + b).

2. Start with the identity:

(a – b)² = (a + b)² – 4ab

3. Substitute the given values:

2² = (a + b)² – 4 × 3

4 = (a + b)² – 12

4. Solve for (a + b)²: 

(a + b)² = 4 + 12

(a + b)² = 16

5. Take the square root on both sides:

a + b = ±4

The value of a + b is either 4 or –4.