Question

if a,b,c are all non zero and a+b+c =0,prove that a^2/bc+b^2/ac+c^2/ab=3

Answer 1

We know that if a+b+c =0 , then a³ + b³ + c³ = 3abc

Now, we have:
LHS = a2/bc+b2/ca+c2/ab
= a³+b³+c³/abc
= 3abc/abc
= 3 = RHS
Hence, proved

Answer 2

We know that if a+b+c =0 , then a³ + b³ + c³ = 3abc

Now, we have:

LHS = a2/bc+b2/ca+c2/ab

= a³+b³+c³/abc

= 3abc/abc

= 3 = RHS

Hence, proved