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If a2 + b2 + c2 = 2 (a + b + c) – 3, then the value of a + b + c is :
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- 2
- –1
- 1
- –2
Correct Option: B
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
[If x2 + y2 + z2 = 0 ⇒ x = 0, y = 0, z = 0]
∴ a + b + c = 1 – 1 – 1 = –1
