Question 127
Let $(x, y, z)$ be a triple of positive real numbers satisfying
$$
xyz = 1 \quad \text{and} \quad \frac{y}{z}(y-x^2) + \frac{z}{x}(z-y^2) + \frac{x}{y}(x-z^2) = 0,
$$
and $t_1, t_2$ and $t_3$ be the smallest, the median and the largest of $x, y, z$, respectively. Find the smallest possible value of
$$
\frac{t_1 + t_3}{t_2}.
$$
$$
xyz = 1 \quad \text{and} \quad \frac{y}{z}(y-x^2) + \frac{z}{x}(z-y^2) + \frac{x}{y}(x-z^2) = 0,
$$
and $t_1, t_2$ and $t_3$ be the smallest, the median and the largest of $x, y, z$, respectively. Find the smallest possible value of
$$
\frac{t_1 + t_3}{t_2}.
$$