If a2 + b2 + c2 + 3 = 2 (a – b

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If a² + b² + c² + 3 = 2 (a – b – c), then the value of 2 a – b + c is :

1. 3
2. 4
3. 0
4. 2

Correct Option: D

a² + b² + c² + 3 = 2a – 2b – 2c
⇒ a² – 2a + 1 + b² + 2b + 1 + c² + 2c + 1 = 0
⇒ (a – 1)² + (b + 1)² + (c + 1)² = 0
∴ a – 1 = 0 ⇒ a = 1
b + 1 = 0 ⇒ b = –1
c + 1 = 0 ⇒ c = –1
∴ 2a – b + c = 2 + 1 – 1 = 2