If a + b + c = m and 1/a + 1/b + 1/c , then average of a2, b2, c2 is?

Answer: Option B

$$\begin{array}{rl}& a+b+c=m\\ & \Rightarrow \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\\ & \Rightarrow \frac{ab+bc+ca}{abc}=0\\ & \Rightarrow ab+bc+ca=0\\ & {\left(a+b+c\right)}^2=a^2+b^2+c^2+2\left(ab+bc+ca\right)\\ & \Rightarrow m^2=a^2+b^2+c^2\\ & \Rightarrow \frac{m^2}{3}=\frac{a^2+b^2+c^2}{3}\end{array}$$