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If a2 + b2 + c2 = 2 (a – b – c) – 3 then the value of 2a – 3b + 4c is
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- 3
- 1
- 2
- 4
Correct Option: B
As per the given question , we have
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
[If x2 + y2 + z2 = 0 ⇒ x = 0; y = 0; z = 0]
∴ a – 1 = 0 ⇒ a = 1
b + 1 = 0 ⇒ b = – 1
c + 1 = 0 ⇒ c = – 1
∴ 2a – 3b + 4c = 2 + 3 – 4 = 1
