$$\frac{{m - {a^2}}}{{{b^2} + {c^2}}}$$   + $$\frac{{m - {b^2}}}{{{c^2} + {a^2}}}$$   + $$\frac{{m - {c^2}}}{{{a^2} + {b^2}}}$$   = 3, then the value of m is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{m - {a^2}}}{{{b^2} + {c^2}}} + \frac{{m - {b^2}}}{{{c^2} + {a^2}}} + \frac{{m - {c^2}}}{{{a^2} + {b^2}}} = 3 \cr & \Rightarrow m = ? \cr & \Rightarrow \frac{{m - {a^2}}}{{{b^2} + {c^2}}} + \frac{{m - {b^2}}}{{{c^2} + {a^2}}} + \frac{{m - {c^2}}}{{{a^2} + {b^2}}} = 1 + 1 + 1 \cr & {\text{Put }}m = {a^2} + {b^2} + {c^2}{\text{ from option (B)}} \cr} $$
$${\text{L}}{\text{.H}}{\text{.S}}{\text{. = }}\frac{{{a^2} + {b^2} + {c^2} - {a^2}}}{{{b^2} + {c^2}}} + $$      $$\frac{{{a^2} + {b^2} + {c^2} - {b^2}}}{{{c^2} + {a^2}}} + $$    $$\frac{{{a^2} + {b^2} + {c^2} - {c^2}}}{{{a^2} + {b^2}}}$$
$$\eqalign{ & \Rightarrow \frac{{{b^2} + {c^2}}}{{{b^2} + {c^2}}} + \frac{{{a^2} + {c^2}}}{{{c^2} + {a^2}}} + \frac{{{a^2} + {b^2}}}{{{a^2} + {b^2}}} \cr & \Rightarrow 1 + 1 + 1 = {\text{R}}{\text{.H}}{\text{.S}}{\text{.}} \cr & \Rightarrow m = {a^2} + {b^2} + {c^2} \cr} $$