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

SInce solving this problem algebraically is a very tedious process, let us put some values for a,b, and c. Then, we will try to match the options.

Let a =1, b = 2 and c=3.

$$\frac{m-1}{13}+\frac{m-4}{10}+\frac{m-9}{5}=3$$

Taking LCM, we get,

$$\frac{10m-10+13m-52+26m-234}{130}=3$$

$$49m = 390 + 296$$

$$49m = 686$$

$$m = 14$$

Substituting a,b and c in options, only option C gives 14 as the answer. Hence, option C is the right answer.