If a² + b² + c² = ab + bc + ca, then the value of $$\frac{{a + c}}{b}$$  is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to the question,}} \cr & {a^2} + {b^2} + {c^2} = ab + bc + ca \cr & {\text{Put }}a = 1 \cr & b = 1 \cr & c = 1 \cr & \therefore {a^2} + {b^2} + {c^2} = ab + bc + ca \cr & \Rightarrow {1^2} + {1^2} + {1^2} = 1 \times 1 + 1 \times 1 + 1 \times 1 \cr & \Rightarrow 1 + 1 + 1 = 1 + 1 + 1 \cr & \Rightarrow 3 = 3{\text{ }}\left( {{\text{Satisfy}}} \right) \cr & \therefore \frac{{a + c}}{b} \cr & = \frac{{1 + 1}}{1} \cr & = 2 \cr} $$