Question 80
Let $a$, $b$ and $c$ be positive real numbers such that
$$
a^2 + b^2 - c^2 = \sqrt{3}ab, \quad a^2 - b^2 + c^2 = \sqrt{2}ac.
$$
Determine the ratio $b : c$. (Hong Kong 2002)
$$
a^2 + b^2 - c^2 = \sqrt{3}ab, \quad a^2 - b^2 + c^2 = \sqrt{2}ac.
$$
Determine the ratio $b : c$. (Hong Kong 2002)