If p3 - q3 = (p – q){(p – q)2

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If p³ - q³ = (p – q){(p – q)² – xpq} then find the value of x

1. 3
2. –3
3. 1
4. –1

Correct Option: B

p³ - q³ = (p – q){(p – q)² – xpq}
⇒ (p – q)(p² + q² + pq) = (p – q)(p² + q² – 2pq – xpq)
⇒ (p² + q² + pq) = p² + q² – (2 + x) pq
∴ – (2 + x) = 1
⇒ x = –2 – 1 = –3