Question

If a b c are all non zero and a+b+c=0 prove that a2/bc+b2/ca+c2/ab=3

Answer 1

Answer:

Given- a, b, c are all non zero and a+b+c=0

To prove= a^2/bc+b^2/ca+c^2/ab=3

Proof:

LHS- a^2/bc+b^2/ca+c^2/ab

LCM of bc, ca,and=ABC

=a^3+b^3+c^3/ABC

=3ABC/ABC

=3

[given a+b+c=0 and if a+b+c=0 then a^3+b^3+c^3=3abc]