conjunto de números reais x que satisfazem a inequação |x² -2|<1
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Olá, acompanhe as operações:
![|x^2-2|\ \textless \ 1 \\ \\ -1\ \textless \ x^2-2\ \textless \ 1 \\ \\ -1+2\ \textless \ x^2\ \textless \ 1+2 \\ \\ 1\ \textless \ x^2\ \textless \ 3 \\ \\ \sqrt{1} \ \textless \ x \ \textless \ \sqrt{3} \\ \\ 1 \ \textless \ x \ \textless \ \sqrt{3} \\ \\ \boxed{\boxed{ ] \, \, 1,\sqrt{3} \, \, [ \, \, \, \to \, \, \, (x \, \in \, \mathbb{R} \, | \, 1 \ \textless \ x \ \textless \ \sqrt{3} ) }}](https://tex.z-dn.net/?f=%7Cx%5E2-2%7C%5C+%5Ctextless+%5C+1+%5C%5C+%5C%5C+-1%5C+%5Ctextless+%5C+x%5E2-2%5C+%5Ctextless+%5C+1+%5C%5C+%5C%5C+-1%2B2%5C+%5Ctextless+%5C+x%5E2%5C+%5Ctextless+%5C+1%2B2+%5C%5C+%5C%5C+1%5C+%5Ctextless+%5C+x%5E2%5C+%5Ctextless+%5C+3+%5C%5C+%5C%5C+%5Csqrt%7B1%7D+%5C+%5Ctextless+%5C++x+%5C+%5Ctextless+%5C++%5Csqrt%7B3%7D+%5C%5C+%5C%5C+1+%5C+%5Ctextless+%5C++x+%5C+%5Ctextless+%5C++%5Csqrt%7B3%7D+%5C%5C+%5C%5C+%5Cboxed%7B%5Cboxed%7B+%5D+%5C%2C+%5C%2C+1%2C%5Csqrt%7B3%7D+%5C%2C+%5C%2C+%5B+%5C%2C+%5C%2C+%5C%2C+%5Cto+%5C%2C+%5C%2C+%5C%2C+%28x+%5C%2C+%5Cin+%5C%2C+%5Cmathbb%7BR%7D+%5C%2C+%7C+%5C%2C+1+%5C+%5Ctextless+%5C++x+%5C+%5Ctextless+%5C++%5Csqrt%7B3%7D+%29+%7D%7D "|x^2-2|\ \textless \ 1 \\ \\ -1\ \textless \ x^2-2\ \textless \ 1 \\ \\ -1+2\ \textless \ x^2\ \textless \ 1+2 \\ \\ 1\ \textless \ x^2\ \textless \ 3 \\ \\ \sqrt{1} \ \textless \ x \ \textless \ \sqrt{3} \\ \\ 1 \ \textless \ x \ \textless \ \sqrt{3} \\ \\ \boxed{\boxed{ ] \, \, 1,\sqrt{3} \, \, [ \, \, \, \to \, \, \, (x \, \in \, \mathbb{R} \, | \, 1 \ \textless \ x \ \textless \ \sqrt{3} ) }}")
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