If $$\frac{1}{p} + \frac{1}{q}$$  = $$\frac{1}{{p + q}}{\text{,}}$$   then the value of p³ - q³ is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{1}{p} + \frac{1}{q} = \frac{1}{{p + q}} \cr & \Rightarrow \frac{{p + q}}{{pq}} = \frac{1}{{p + q}} \cr & \Rightarrow {\left( {p + q} \right)^2} = pq \cr & \Rightarrow \left( {{p^2} + {q^2} + 2pq - pq} \right) = 0 \cr & \Rightarrow \left( {{p^2} + {q^2} + pq} \right) = 0 \cr & {\text{Multiply by }}\left( {p - q} \right){\text{ both side}} \cr & \Rightarrow \left( {p - q} \right)\left( {{p^2} + {q^2} + pq} \right) = \left( {p - q} \right) \times 0 \cr & \Rightarrow {p^3} - {q^3} = 0 \cr} $$