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If a, b, c are real and a2 + b2 + c2 = 2 (a – b – c) – 3, then the value of 2a – 3b + 4c is
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- –1
- 0
- 1
- 2
Correct Option: C
a2 + b2 + c2 = 2a – 2b – 2c – 3
⇒ a2 – 2a + b2 + 2b + c2 + 2c + 1 + 1 + 1 = 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
and c + 1 = 0 ⇒ c = –1
∴ 2a – 3b + 4c = 2 + 3 – 4 = 1
