Question

If p + q = 8 and p - q = 4, find:
pq

Answer 1

(p + q)² = (8)²
p² + q² + 2pq = 64      ...(i)
(p - q)² = (4)²
p² + q² - 2pq = 16
p² + q² = 16 + 2pq       ...(ii)
Using (ii) in (i), we get :
16 + 2pq + 2pq = 64
⇒ 4pq 
= 64 - 16
= 48
⇒ pq = 12.