If a + b + c = 9 (where a, b, c are real numbers) then the minimum value of a² + b² + c² is?

$$\eqalign{ & a + b + c = 9 \cr & {\text{For minimum value}} \cr & a = b = c \cr & \Rightarrow 3a = 9 \cr & \Rightarrow a = \frac{9}{3} \cr & \Rightarrow a = 3 \cr & {\text{For minimum value}} \cr & a = b = c = 3 \cr & \therefore {a^2} + {b^2} + {c^2} \cr & \Rightarrow {3^2} + {3^2} + {3^2} \cr & \Rightarrow 9 + 9 + 9 \cr & \Rightarrow 27 \cr} $$