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