Determination Δ=\(\begin{vmatrix}b + c &c + a &a + b\\[0.3em]c + a & a + b&b + c\\[0.3em]a + b&b + c & c + a\end{vmatrix}\)

Question

If a, b, c are real, find the factors of the determination

Δ  = \(\begin{vmatrix} b + c &c + a &a + b \\[0.3em] c + a & a + b &b + c\\[0.3em] a + b &b + c & c + a \end{vmatrix}\)

Answer 1

then a + b + c = 0 or a = b = c.