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If a, b, c are real numbers and a2 + b2 + c2 = 2 (a – b – c) – 3, then the value of a + b + c is
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- – 1
- 1
- 3
- 0
Correct Option: A
a2 + b2 + c2 = 2a – 2b – 2c – 3
⇒ a2 – 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
⇒ (a – 1)2 + (b + 1)2 + (c + 1)2 = 0
⇒ a – 1 = 0, b + 1 = 0, c + 1 = 0
⇒ a = 1, b = –1, c = –1
∴ a + b + c = 1 – 1 – 1 = –1
