Question

a+b+c=0 prove that a^2/bc+b^2/ac+c^2/ab=3

Answer 1

a2/bc + b2/ac + c2/ab = a3 + b3 + c3/abc

=>a3 + b3+ c3= 3abc

=>a3 + b3+ c3 - 3abc = 0

now, a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca)

therefore, (a + b + c) (a2 + b2 + c2 − ab − bc − ca)  = 0

now, a + b+ c = 0

therefore, a3 + b3 + c3 - 3abc = 0

hence proved.

hope it helps!!

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