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

Answer: Option D

$$\begin{array}{rl}& a^2+b^2+c^2=2\left(a-b-c\right)-3\\ & \Rightarrow a^2+b^2+c^2=2a-2b-2c-3\\ & \Rightarrow a^2+b^2+c^2-2a+2b+2c+3=0\\ & \Rightarrow a^2-2a+1+b^2+2b+1+c^2+2c+1=0\\ & \Rightarrow {\left(a-1\right)}^2+{\left(b+1\right)}^2+{\left(c+1\right)}^2=0\\ & {\left(a-1\right)}^2=0{\left(b+1\right)}^2=0{\left(c+1\right)}^2=0\\ & \Rightarrow a-1=0\Rightarrow b+1=0\Rightarrow c+1=0\\ & \Rightarrow a=1\Rightarrow b=-1\Rightarrow c=-1\\ & \therefore a+b+c\\ & =1-1-1\\ & =-1\end{array}$$