If a + b + c = m and $$\frac{1}{a}$$ + $$\frac{1}{b}$$ + $$\frac{1}{c}{\text{,}}$$ then average of a², b², c² is?

A. $${m^2}$$

B. $$\frac{{{m^2}}}{3}$$

C. $$\frac{{{m^2}}}{9}$$

D. $$\frac{{{m^2}}}{{27}}$$

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & a + b + c = m \cr & \Rightarrow \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 0 \cr & \Rightarrow \frac{{ab + bc + ca}}{{abc}} = 0 \cr & \Rightarrow ab + bc + ca = 0 \cr & {\left( {a + b + c} \right)^2} = {\text{ }}{a^2} + {b^2} + {c^2} + 2\left( {ab + bc + ca} \right) \cr & \Rightarrow {m^2} = {\text{ }}{a^2} + {b^2} + {c^2} \cr & \Rightarrow \frac{{{m^2}}}{3} = {\text{ }}\frac{{{a^2} + {b^2} + {c^2}}}{3} \cr} $$