If a − b = 3 and a^2 + b^2 = 29, find ab.

Concept / Approach

• Use the identity (a − b)^2 = a^2 + b^2 − 2ab.

Step-by-step calculation
(a − b)^2 = 3^2 = 9a^2 + b^2 − 2ab = 29 − 2ab = 92ab = 29 − 9 = 20 ⇒ ab = 10

Common pitfalls

• Using (a + b)^2 identity by mistake; here we need (a − b)^2.

Final Answer
10