Question 111
Three different nonzero real numbers $a$, $b$, $c$ satisfy the equations
$$
a + \frac{2}{b} = b + \frac{2}{c} = c + \frac{2}{a} = p
$$
where $p$ is a real number. Prove that $abc + 2p = 0$.
$$
a + \frac{2}{b} = b + \frac{2}{c} = c + \frac{2}{a} = p
$$
where $p$ is a real number. Prove that $abc + 2p = 0$.