If 2p + q = 19 and 8p3 + q3 = 361, then find the value of pq.

If 2p + q = 19 and 8p³ + q³ = 361

a³ + \(\frac{1}{a^3}\) = (a + \(\frac{1}{a}\))³ – 3(a + \(\frac{1}{a}\))

361 = 19³ - 3  × 19  × 2pq

2pq = 114

pq = 57