Solving $L= \frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ priveded $a+b+c=0$ 
Let $a,b,c$ be such that $a+b+c=0$ and suppose that 
  $$L= \frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}.$$
  Find the value of $L$.

I can only see the symmetry of these function but cannot solve it.

Since $a+b+c|(a^3+b^3+c^3-3abc)$, $a+b+c = 0 \implies a^3+b^3+c^3 = 3abc$.
Then Wolfram Alpha says that this gives the sum as $1$.
