If $$a = \frac{{{b^2}}}{{b - a}}{\text{,}}$$   then the value of a³ + b³ is?

Solution (By Examveda Team)

$$\eqalign{ & a = \frac{{{b^2}}}{{b - a}} \cr & \Rightarrow a\left( {b - a} \right) = {b^2} \cr & \Rightarrow ab - {a^2} = {b^2} \cr & \Rightarrow {a^2} + {b^2} - ab = 0 \cr & \Rightarrow {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right) \cr & \Rightarrow {a^3} + {b^3} = 0 \cr} $$