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For real a, $b, c$ with $a^{2} + b^{2} + c^{2} = 2 (a - b - c) - 3$ , find $2 a - 3 b + 4 c$ .

Competition practiceAlgebra

A5
B1
C−1
D9

Step-by-Step Solution

Rearranging:

(a - 1)^{2} + (b + 1)^{2} + (c + 1)^{2} = 0

, so

a = 1, b = c = - 1

. Then

2 + 3 - 4 = 1

.

Answer: B) 1

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