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Question
If p + q = 8 and p - q = 4, find:
pq
Solution
(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.
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