Question 98
If $a$, $b$, $c$, $x$ are real numbers such that $a b c \neq 0$ and
$$
\frac{x b + (1-x) c}{a} = \frac{x c + (1-x) a}{b} = \frac{x a + (1-x) b}{c}
$$
then prove that either $a + b + c = 0$ or $a = b = c$.
$$
\frac{x b + (1-x) c}{a} = \frac{x c + (1-x) a}{b} = \frac{x a + (1-x) b}{c}
$$
then prove that either $a + b + c = 0$ or $a = b = c$.