Question

If a – b = 2 and ab = 3, find the value of a² + b².

Answer 1

Given: a – b = 2 and ab = 3

Step-wise calculation:

1. Recall the identity:

(a – b)² = a² – 2ab + b²

2. Substitute the given values:

2² = a² – 2(3) + b² 

4 = a² – 6 + b²

3. Rearrange to find a² + b²: 

a² + b² = 4 + 6

a² + b² = 10