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If 3(a² + b² + c²) = (a + b + c)², then the relation between a, b and c is
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- a ≠ b ≠ c
- a = b ≠ c
- a ≠ b = c
- a = b = c
Correct Option: D
3a² + 3b² + 3c² = (a + b + c)²
⇒ 3a² + 3b² + 3c² = a² + b² + c² + 2ab + 2bc + 2ac
⇒ 3a² + 3b² + 3c² – a² – b² – c² – 2ab – 2bc – 2ac = 0
⇒ 2a² + 2b² + 2c² – 2ab – 2bc – 2ac = 0
⇒ a² + b² – 2ab + b² + ² – 2bc + a² + c² – 2ac = 0
⇒ (a – b)² + (b – c)² + (c – a)² = 0
⇒ a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a
∴ a = b = c
