1\\\\ 2) \ x - 1 < 0, \ x < 1 \\\\ x^2 - 1 \geq 0, \ (x - 1)(x + 1) \geq 0, \ x \in (-\infty; -1] \cup [1; +\infty)\\\\ x \leq -1\\\\ \boxed{ \mathbb{OTBET}: x \in (-\infty;-1] \cup (1; +\infty)}" alt="x - 1 < \sqrt{x^2 - 1}\\\\ 1) \ x -1 \geq 0, \ x \geq 1\\\\ x^2 -2x + 1 < x^2 - 1\\\\ -2x < -2 | : -2\\\\\ x > 1\\\\ 2) \ x - 1 < 0, \ x < 1 \\\\ x^2 - 1 \geq 0, \ (x - 1)(x + 1) \geq 0, \ x \in (-\infty; -1] \cup [1; +\infty)\\\\ x \leq -1\\\\ \boxed{ \mathbb{OTBET}: x \in (-\infty;-1] \cup (1; +\infty)}" align="absmiddle" class="latex-formula">