Question 34
Let $x_1$, $x_2$, $x_3$ and $y_1$, $y_2$, $y_3$ are 6 positive real numbers such that
$$
x_1 + x_2 + x_3 = y_1y_2y_3 \text{ and } y_1 + y_2 + y_3 = x_1x_2x_3.
$$
Find the minimum value of $T = x_1y_1 + x_2y_2 + x_3y_3$.
$$
x_1 + x_2 + x_3 = y_1y_2y_3 \text{ and } y_1 + y_2 + y_3 = x_1x_2x_3.
$$
Find the minimum value of $T = x_1y_1 + x_2y_2 + x_3y_3$.