Answer :

a2 + b2 + c2 – ab – bc – ca = 0


Multiplying both sides by 2 we get


2 (a2 + b2 + c2 – ab – bc – ca ) = 0


(a2 + b2 - 2ab) + ( b2 + c2 - 2bc) + (c2 + a2 -2ac) = 0


The individual terms inside the brackets can be expressed as a whole square


(a – b)2 + (b – c)2 + (c – a)2 = 0


Since a, b, c are rational and none of the term is equal to zero so each of the terms inside the bracket must individually be equal to zero


a – b = 0


a = b


b – c = 0


b = c


c – a = 0


c = a


So together we can say that


a = b = c


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