Question

If a+b+c=0 for a,b,c then prove a²/bc+b²/ca+c²/ab=3.

Answer 1

according to the identity if a+b+c=0
then a3+b3+c3=3abc
a3+b3+c3/abc=3
a2*a/bc*a+b2*b/ca*b+c2*c/ab*c=3
cancel a,b,c in all the fraction then you get
a²/bc+b²/ca+c²/ab=3.
hence proved