Question

i did not understand how did a^2+b^2+c^2-ab-bc-ca+0 come?????last fourth step...

Answer 1

Answer:

 a² + b² + c² – ab – bc – ca = 0

Multiply both sides with 2, we get

2( a² + b² + c² – ab – bc – ca) = 0

⇒ 2a² + 2b² + 2c² – 2ab – 2bc – 2ca = 0

⇒ (a² – 2ab + b²) + (b² – 2bc + c²) + (c² – 2ca + a²) = 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.