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