Question 106
$a$, $b$ and $c$ are non-zero real numbers such that $\frac{a+b}{c} = \frac{b+c}{a} = \frac{c+a}{b}$.
(1) Prove that $a^3 + b^3 + c^3 \neq 0$.
(2) Determine all possible values of the expression $\frac{(a+b)(b+c)(c+a)}{a^3 + b^3 + c^3}$.
(1) Prove that $a^3 + b^3 + c^3 \neq 0$.
(2) Determine all possible values of the expression $\frac{(a+b)(b+c)(c+a)}{a^3 + b^3 + c^3}$.