Given a - b = 2, a³ - b³ = 26, then (a + b)² is?

Solution (By Examveda Team)

$$\eqalign{ & a - b = 2{\text{ }} \cr & {a^3} - {b^3} = 26 \cr & \Rightarrow {a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right) \cr & \Rightarrow 26 = \left( 2 \right)\left( {{a^2} + ab + {b^2}} \right) \cr & \Rightarrow 13 = \left( {{a^2} + ab + {b^2}} \right)\,....(i) \cr & \Rightarrow 4 = 13 + ab \cr & \Rightarrow {\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab \cr & \Rightarrow {\left( 2 \right)^2} = {a^2} + {b^2} + ab - 3ab \cr & \Rightarrow 3ab = 9 \cr & \Rightarrow ab = 3 \cr & \therefore {\left( {a + b} \right)^2} \cr & = {\left( {a - b} \right)^2} + 4ab \cr & = 4 + 4 \times 3 \cr & = 16 \cr} $$