If `a ,\ b ,\ c` are real numbers such that `|b+cc+a a+b c+a a+bb+c a+bb+cc+a|=0` , then show that either `a+b+c=0` or, `a=b=c` .

Explanation

To solve the problem, we need to analyze the determinant given in the question:

\[ |b + c \quad c + a \quad a + b| \]
\[ |c + a \quad a + b \quad b + c| \]
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