If $$\frac{{m - 3{a^3}}}{{{b^3} + {c^3}}}$$  $$+$$ $$\frac{{m - 3{b^3}}}{{{c^3} + {a^3}}}$$  $$+$$ $$\frac{{m - 3{c^3}}}{{{a^3} + {b^3}}}$$   = 9, then the value of m is?

A. $${a^2} + {b^2} + {c^2}$$

B. $${\text{2}}{a^2} + 2{b^2} + 2{c^2}$$

C. $${\text{3}}{a^2} + 3{b^2} + 3{c^2}$$

D. 2

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Put }}a = b = c = 1 \cr & {\text{Then we have }} \cr & \frac{{m - 3}}{2}{\text{ + }}\frac{{m - 3}}{2}{\text{ + }}\frac{{m - 3}}{2} = 9{\text{ }} \cr & m = 9 \cr} $$
Now, putting values of a, b, c in option,
Only option (C) gives value of m = 9
So, option (C) is correct.