Question 144
Let $x, y, z \in \mathbb{R} - \{1\}$ be real numbers such that $x + y + z = 4$, $x^{2} + y^{2} + z^{2} = 6$ and $xyz = a$, $a \in \mathbb{R} - \{2\}$.
Compute the value of the expression
$$
E = \frac{1}{xy + z - 3} + \frac{1}{yz + x - 3} + \frac{1}{zx + y - 3}.
$$
Compute the value of the expression
$$
E = \frac{1}{xy + z - 3} + \frac{1}{yz + x - 3} + \frac{1}{zx + y - 3}.
$$