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

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

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

Correct Option: B

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
and, c – 1 = 0 ⇒ c = 1
∴ a + b + c = 3