If p³ - q³ = (p - q){(p -q)² + xpq}, then the value of x is?

A. 1

B. -1

C. 3

D. 2

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \Rightarrow {p^3} - {q^3} = \left( {p - q} \right)\left\{ {{{\left( {p - q} \right)}^2} + xpq} \right\} \cr & \Rightarrow \left( {p - q} \right)\left\{ {{p^2} + {q^2} + pq} \right\} = \left( {p - q} \right)\left\{ {{p^2} + {q^2} - 2pq + xpq} \right\} \cr & \Rightarrow {p^2} + {q^2} + pq = {p^2} + {q^2} - 2pq + xpq \cr & \Rightarrow 3pq = xpq \cr & \Rightarrow x = 3 \cr} $$