If the number p is 5 more than q and the sum of the squares

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If the number p is 5 more than q and the sum of the squares of p and q is 55, then the product of p and q is

p = q + 5
⇒ p – q = 5
p² + q² = 55
∴ (p – q)² + 2pq = 55
⇒ 25 + 2 pq = 55
⇒ 2 pq = 30
⇒ pq = 15