Question 82
Let $a, b, c, d$ be four real numbers such that $|a| \gt 1, |b| \gt 1, |c| \gt 1$ and $|d| \gt 1$. Suppose that $(a+1)(b+1)(c+1)(d+1) = (a-1)(b-1)(c-1)(d-1)$. Show that
$$
\frac{1}{a-1} + \frac{1}{b-1} + \frac{1}{c-1} + \frac{1}{d-1} \gt 0
$$
$$
\frac{1}{a-1} + \frac{1}{b-1} + \frac{1}{c-1} + \frac{1}{d-1} \gt 0
$$