If a, b and c are real numbers, and `Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0`. Show that either `a+b+c=0` or `a=b=c`

Explanation

To solve the problem, we need to show that if the determinant \(\Delta = |[b+c, c+a, a+b], [c+a, a+b, b+c], [a+b, b+c, c+a]| = 0\), then either \(a + b + c = 0\) or \(a = b = c\).

### Step-by-Step Solution:

1. **Write the Determinant**:
\[
\Delta = \begin{vmatrix}
b+c & c+a & a+b \\
...