If a2 + b2 + c2 = 2 (a – b – c)

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If a² + b² + c² = 2 (a – b – c) – 3, then the value of 4a – 3b + 5c is

1. 2
2. 3
3. 5
4. 6

Correct Option: A

a² + b² + c² = 2 (a – b – c) – 3
⇒ a² + b² + c² – 2a + 2b + 2c + 3 = 0
⇒ 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
∴ 4a – 3b + 5c = 4 × 1 – 3 × (–1) + 5 (–1) = 4 + 3 – 5 = 2