If a + b + c = 0 then prove that .

Given a + b + c = 0

Proof:

Using formula

(a + b)² = a² + b² + 2ab and expanding the LHS

Multiplying and dividing the expression by 3abc, so the resulting equation is

Now making a pair of ab² and a²b and taking the common factor.

Similarly, for other terms, we get,

a + b + c = 0, so a + b = – c, b + c = – a, a + c = – b

Hence proved LHS = RHS