Question

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

Answer 1

When a+b+c=0, a³+b³+c³ = 3abc.
R.T.P.:a²/bc+b²/ca+c²/ab=3
Proof: a²/bc+b²/ca+c²/ab
        = a³+b³+c³/abc    [abc is the L.C.M. of bc, ca and ab]
        = 3abc/abc          [∵ a³+b³+c³ = 3abc, when a+b+c=0]
        = 3
∴proved