If $$\frac{a}{b} + \frac{b}{a} = 1{\text{,}}$$   then the value of a³ + b³ will be?

Solution (By Examveda Team)

$$\eqalign{ & {a^2} + {b^2} = ab\,........(i) \cr & {a^2} + {b^2} - ab = 0 \cr & \because {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)\,.....(ii) \cr & {\text{From equation (i) and (ii)}} \cr & \Rightarrow {a^3} + {b^3} = \left( {a + b} \right)\left( 0 \right) \cr & \Rightarrow {a^3} + {b^3} = 0 \cr} $$