Question : If $a, b, c$ are real numbers and $a^{2}+b^{2}+c^{2}=2(a-b-c)-3,$ then the value of $a+b+c$ is:
Option 1: –1
Option 2: 1
Option 3: 3
Option 4: 0
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Correct Answer: –1
Solution :
Given: $a, b$ and $c$ are real numbers.
$a^{2}+b^{2}+c^{2}=2(a-b-c)-3$
$⇒a^{2}+b^{2}+c^{2}-2a+2b+2c+3=0$
$⇒(a-1)^{2}+(b+1)^{2}+(c+1)^{2}=0$
$⇒a=1, b=-1, c=-1$
$a+b+c=1-1-1=-1$
Hence, the value of $a+b+c$ is –1.
Hence, the correct answer is –1.
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