If a + b = 1 and a³ + b³ + 3ab = k, then the value of k is?

Solution (By Examveda Team)

$$\eqalign{ & a + b = 1 \cr & {\text{By cubing,}} \cr & {a^3} + {b^3} + 3ab\left( {a + b} \right) = {1^3} \cr & \Rightarrow {a^3} + {b^3} + 3ab = 1\left[ {\because a + b = 1} \right] \cr & \Rightarrow {a^3} + {b^3} + 3ab = k \cr & {\text{From above both equations,}} \cr & k = 1 \cr} $$