Question 39
Let $a, b, c \in (0, \infty)$, not all equal. Solve the equation
$$
(a^x + b^x + c^x) (a^{-x} + b^{-x} + c^{-x}) = 3 + \frac{a^2 + b^2}{ab} + \frac{b^2 + c^2}{bc} + \frac{c^2 + a^2}{ca}.
$$
$$
(a^x + b^x + c^x) (a^{-x} + b^{-x} + c^{-x}) = 3 + \frac{a^2 + b^2}{ab} + \frac{b^2 + c^2}{bc} + \frac{c^2 + a^2}{ca}.
$$