Find the value of a2/bc + b2/ca + c2/ab.

If a + b + c = 0, then find the value of a²/bc + b²/ca + c²/ab.

Answer :

It is given that

a + b + c = 0

We can write it as

a³ + b³ + c³ – 3abc = 0

a³ + b³ + c³ = 3abc

Now dividing by abc on both sides

a³/abc + b³/abc + c³/abc = 3

By further calculation

a²/bc + b²/ac + c²/ab = 3

Therefore, the value of a²/bc + b²/ca + c²/ab is 3.

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