If p − q = 6 and p^2 + q^2 = 116 , what is the value of pq ?

Question

If p − q = 6 and p² + q² = 116 , what is the value of pq ?

A. 50

B. 40

C. 30

D. 20

Answer: B. 40

Solution:

{reference: basic algebraic formulas}

(p − q)² = p² − 2pq + q²

⇒ 62 = 116 − 2pq

⇒ 36 = 116 − 2pq

⇒ 2pq = 80

⇒ pq = 40

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