\(\left|x^2-2x-2\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-2=5\\x^2-2x-2=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-2.x.1+1^2-3=5\\x^2-2.x.1+1^2-3=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^2=5+3\\\left(x-1\right)^2=-5+3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^2=8\\\left(x-1\right)^2=-2\end{matrix}\right.\)
\(\Leftrightarrow\left(x-1\right)^2=8\)
\(\Leftrightarrow x-1=\sqrt{8}\)
\(\Leftrightarrow x=\sqrt{8}+1\)
\(\Leftrightarrow x=1+2\sqrt{2}\)
\(\Leftrightarrow x\approx3,8\)
Vậy : \(x\approx3,8\).
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