Question

O conjunto de todos os números reais x satisfazem a inequação | x² - 2| < 1 é

Answer 1

$|x^2-1|\ \textless \ 1\iff -1\ \textless \ x^2-1\ \textless \ 1\\ \\ |x^2-1|\ \textless \ 1\iff 1-1\ \textless \ x^2\ \textless \ 1+1\\ \\ |x^2-1|\ \textless \ 1\iff 0\ \textless \ x^2\ \textless \ 2\\ \\ |x^2-1|\ \textless \ 1\iff 0\ \textless \ x\ \textless \ \sqrt2 \vee -\sqrt{2}\ \textless \ x\ \textless \ 0\\ \\ \\ \boxed{|x^2-1|\ \textless \ 1\iff x\in(-\sqrt{2},0)\cup (0,\sqrt{2})}$

Answer 2

Resposta:

( -$\sqrt{3}$,-1) ∪ (1,$\sqrt{3\\}$)

Explicação passo-a-passo: