Question 2
Let $x$, $y$, $z$ be real numbers with $xyz = 1$, all different from $1$. Prove that $$
\frac{x^2}{(x-1)^2} + \frac{y^2}{(y-1)^2} + \frac{z^2}{(z-1)^2} \ge 1
$$ and show that equality holds for infinitely many choices of rational numbers $x$, $y$, $z$.
\frac{x^2}{(x-1)^2} + \frac{y^2}{(y-1)^2} + \frac{z^2}{(z-1)^2} \ge 1
$$ and show that equality holds for infinitely many choices of rational numbers $x$, $y$, $z$.