Q3 of 65 Page 145

Short answer type questions:

Let us write the relation of a, b and c if a3 + b3 + c3 – 3abc = 0 and a + b + c ≠ 0.

As we know from the identity that,


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


Since a + b + c ≠ 0, that means,


a2 + b2 + c2 – ab – bc – ca = 0


Multiplying both sides by 2, we get,


a2 + b2 – 2ab + b2 + c2 – 2bc + a2 + c2 – 2ac = 0


⇒ (a – b)2 + (b – c)2 + (a – c)2 = 0


Now this is only possible if:


a – b = 0, b – c = 0 and a – c =0


⇒ a = b = c


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