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

Solution (By Examveda Team)

$${p^3} - {q^3} = \left( {p - q} \right)\left\{ {{p^2} + {q^2} + pq} \right\}$$
$$ \Rightarrow \left( {p - q} \right)\left\{ {{{\left( {p + q} \right)}^2} - xpq} \right\} = $$       $$\left( {p - q} \right)$$ $$\left( {{p^2} + {q^2} + pq} \right)$$
$$\eqalign{ & \Rightarrow {p^2} + {q^2} + 2pq - xpq = {p^2} + {q^2} + pq \cr & \Rightarrow 2pq - pq = xpq \cr & \Rightarrow pq = xpq \cr & \Rightarrow x = 1 \cr} $$