Question 17
The real numbers $x, y, z$, with $x \neq z$, are mutually different and nonzero and they satisfy the following equations:
$$
(x+y)^2 + (2-xy) = 9, \\
(y+z)^2 - (3+yz) = 4.
$$
Determine the value of the expression
$$
A = \left( \frac{x}{y} + \frac{y^2}{x^2} + \frac{z^3}{x^2y} \right) \left( \frac{y}{z} + \frac{z^2}{y^2} + \frac{x^3}{y^2z} \right) \left( \frac{z}{x} + \frac{x^2}{z^2} + \frac{y^3}{z^2x} \right).
$$
$$
(x+y)^2 + (2-xy) = 9, \\
(y+z)^2 - (3+yz) = 4.
$$
Determine the value of the expression
$$
A = \left( \frac{x}{y} + \frac{y^2}{x^2} + \frac{z^3}{x^2y} \right) \left( \frac{y}{z} + \frac{z^2}{y^2} + \frac{x^3}{y^2z} \right) \left( \frac{z}{x} + \frac{x^2}{z^2} + \frac{y^3}{z^2x} \right).
$$