\(a+b+c=0\Rightarrow\left(a+b\right)=-c\Rightarrow\left(a+b\right)^2=\left(-c\right)^2\Leftrightarrow a^2+b^2+2ab=c^2\)
\(\Rightarrow a^2+b^2-c^2=-2ab\)
Tương tự: \(b^2+c^2-a^2=-2bc;\text{ }c^2+a^2-b^2=-2ca\)
\(\Rightarrow VT=-\frac{1}{2bc}-\frac{1}{2ca}-\frac{1}{2ab}=-\frac{1}{2}\left(\frac{a+b+c}{abc}\right)=0=VP\text{ (đpcm)}\)