33. For what values of $r$ is the inequality

$$
\left(r^{2}-1\right) x^{2}+2(r-1) x+1>0
$$

satisfied for all $x$?
33. A quadratic trinomial is positive for any values of $x$ if the coefficient of $x^{2}$ is positive, and the discriminant is negative, i.e., $r^{2}-1>0 (r>0, r>1$.

Answer: $r>1$.