The Total solution for NCERT class 6-12
a2 + b2 + c2 –ab – bc – ca = 02 {a2 + b2 + c2 – ab – be – ca)= 0 (Multiplying by 2)⇒ 2a2 + 2b2 + 2c2– 2ab – 2bc – 2ca = 0⇒ a2 + b2 – 2ab + b2 + c2 –2bc + c2 + a2 – 2ca = 0⇒ (a – b)2 + (b – c)2 + (c – a)2 =0(a – b)2 = 0, then a – b = 0⇒ a = bSimilarly, (b – c)2 = 0, thenb-c = 0⇒ b = cand (c – a)2 = 0, then c-a = 0⇒ c = a∴ a = b– c (d)