If a^{2}+b^{2}+c^{2}=2(a-b-c)-3, then the val | vedclass

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(C) Given equation: $a^{2}+b^{2}+c^{2}=2(a-b-c)-3$Expand the right side: $a^{2}+b^{2}+c^{2}=2a-2b-2c-3$Rearrange the terms to one side: $a^{2}-2a+b^{2

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$1$

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(C) Given equation: $a^{2}+b^{2}+c^{2}=2(a-b-c)-3$Expand the right side: $a^{2}+b^{2}+c^{2}=2a-2b-2c-3$Rearrange the terms to one side: $a^{2}-2a+b^{2}+2b+c^{2}+2c+3=0$Split $3$ into $1+1+1$: $(a^{2}-2a+1)+(b^{2}+2b+1)+(c^{2}+2c+1)=0$Rewrite as perfect squares: $(a-1)^{2}+(b+1)^{2}+(c+1)^{2}=0$Since the sum of squares is zero,each term must be zero: $a-1=0, b+1=0, c+1=0$Solving these gives: $a=1, b=-1, c=-1$Calculate $(a-b+c)$: $1-(-1)+(-1) = 1+1-1 = 1$

If $a^{2}+b^{2}+c^{2}=2(a-b-c)-3,$ then the value of $(a-b+c)$ is

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