a² + b² + c² = ab + bc + ca On multiplying both sides by ‘2’, it becomes 2 ( a² + b² + c² ) = 2 ( ab + bc + ca) 2a² + 2b² + 2c² = 2ab + 2bc + 2ca a² + a² + b² + b² + c² + c² – 2ab – 2bc – 2ca = 0 a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ca = 0 (a² + b² – 2ab) + (b² + c² – 2bc) + (c² + a² – 2ca) = 0 (a – b)² + (b – c)² + (c – a)² = 0 => Since the sum of square is zero then each term should be zero ⇒ (a –b)² = 0, (b – c)² = 0, (c – a)² = 0 ⇒ (a –b) = 0, (b – c) = 0, (c – a) = 0 ⇒ a = b, b = c, c = a ∴ a = b = c. Reply
a² + b² + c² = ab + bc + ca
On multiplying both sides by ‘2’, it becomes
2 ( a² + b² + c² ) = 2 ( ab + bc + ca)
2a² + 2b² + 2c² = 2ab + 2bc + 2ca
a² + a² + b² + b² + c² + c² – 2ab – 2bc – 2ca = 0
a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ca = 0
(a² + b² – 2ab) + (b² + c² – 2bc) + (c² + a² – 2ca) = 0
(a – b)² + (b – c)² + (c – a)² = 0
=> Since the sum of square is zero then each term should be zero
⇒ (a –b)² = 0, (b – c)² = 0, (c – a)² = 0
⇒ (a –b) = 0, (b – c) = 0, (c – a) = 0
⇒ a = b, b = c, c = a
∴ a = b = c.