If a, b, c are real and a2 + b2 + c2 = 2(a - b - c) -3, then the value of 2a - 3b + 4c is?
A. -1
B. 0
C. 1
D. 2
Answer: Option C
Solution(By Examveda Team)
a2 + b2 + c2 = 2(a - b - c) - 3⇒ a2 + b2 + c2 = 2a - 2b - 2c - 3
⇒ a2 + b2 + c2 - 2a + 2b +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
b = -1
c = -1
∴ 2a - 3b + 4c
= 2 × 1 - 3 × (-1) + 4 × (-1)
= 2 + 3 - 4
= 1
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