Question

Calculate `1/(b^2+c^2-a^2) + 1/(c^2+a^2-b^2) + 1/(a^2+b^2-c^2)` , if a+b+c = 0 ?

Answer 1

`0`

Explanation:

Substituting `c=-a-b` in the equation above we get

`1/(2b^2+2ab)+1/(2a^2+2ab)-1/(2ab)=`

`=(a+b-a-b)/(2ab(a+b))=0`