Question 168
Suppose $a$, $b$, $c$ are real numbers such that $abc \neq 0$. Determine $x$, $y$, $z$ in terms of $a$, $b$, $c$ such that
$$
bz + cy = a, \quad cx + az = b, \quad ay + bx = c.
$$
Prove also that
$$
\frac{1-x^2}{a^2} = \frac{1-y^2}{b^2} = \frac{1-z^2}{c^2}.
$$
$$
bz + cy = a, \quad cx + az = b, \quad ay + bx = c.
$$
Prove also that
$$
\frac{1-x^2}{a^2} = \frac{1-y^2}{b^2} = \frac{1-z^2}{c^2}.
$$