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By inspection we see that the two expressions on the LHS are totally symmetric in a,b and c. If we consider them as equations we note that the highest exponent of x is x², so they are quadratic equations in x. We also note that x=a is a solution to both equations and by symmetry also x=b and x=c. But a quadratic equation can have at most only two roots not three, so they are NOT quadratic equations but identities.