Question

Rezolvati in R inecuatia
$|x^2-1|\ \textless \ 1$

Answer 1

Explicație pas cu pas:

Answer 2

$|x^2-1|<1 \\ \\ \Leftrightarrow\,\, -1<x^2-1<1\\ \\ \Leftrightarrow\,\, 0 < x^2 < 2\\ \\ \Leftrightarrow \,\,x^2 > 0\quad \wedge\quad x^2 < 2\\ \\\Leftrightarrow\,\,x\neq 0\quad \wedge\quad x^2 < 2\,\Big|\sqrt{} \\ \\ \Leftrightarrow\,\,x\neq 0\quad \wedge\quad |x| < \sqrt{2}\\ \\\Leftrightarrow\,\,x\neq 0\quad \wedge\quad -\sqrt 2 < x < \sqrt{2}\\ \\\\ \Rightarrow \boxed{x\in \big(-\sqrt 2,\sqrt 2\,\big)\,\backslash\,\big\{0\big\}}$