Question 49
Suppose $x, y, z$ are positive numbers such that
$$
1 = 2xyz + xy + yz + zx.
$$
Prove that there are positive numbers $a, b, c$ such that
$$
x = \frac{a}{b+c}, \quad y = \frac{b}{c+a}, \quad z = \frac{c}{a+b}.
$$
$$
1 = 2xyz + xy + yz + zx.
$$
Prove that there are positive numbers $a, b, c$ such that
$$
x = \frac{a}{b+c}, \quad y = \frac{b}{c+a}, \quad z = \frac{c}{a+b}.
$$