Question

if a+b+c=0 then the value of a^2+b^2+c^2/ab+bc+ca

Answer 1

a+b+c=0
using the identity,
(a+b+c)²=a²+b²+c²+2(ab+bc+ca)
putting the value of a+b+c
0=a²+b²+c²+2(ab+bc+ca)
-2(ab+bc+ca)=a²+b²+c²
a²+b²+c²/ab+bc+ca=  -2