If a² + b² + c² + 3 = 2(a - b - c), then the value of 2a - b + c is?

Solution (By Examveda Team)

$$\eqalign{ & {a^2} + {b^2} + {c^2} + 3 = 2\left( {a - b - c} \right) \cr & \Rightarrow {a^2} + {b^2} + {c^2} + 3 - 2a + 2b + 2c = 0 \cr & \Rightarrow {a^2} - 2a + 1 + {b^2} + 2b + 1 + {c^2} + 2c + 1 = 0 \cr & \Rightarrow {\left( {a - 1} \right)^2} + {\left( {b + 1} \right)^2} + {\left( {c + 1} \right)^2} = 0 \cr & a = 1 \cr & b = - 1 \cr & c = - 1 \cr & \therefore 2a - b + c \cr & = 2 + 1 - 1 \cr & = 2 \cr} $$