3 (a2+b2+c2) = (a+b+c)2 ⇒ 3a2+3b2+3c2 = a2+b2+c2 + 2ab + 2bc + 2ca ⇒ 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 = 0 ⇒ a = b [If x2+y2+z2 = 0, x = 0, y = 0, z = 0] b – c = 0 ⇒ b = c c – a = 0 ⇒ c = a ∴ a = b = c