1.
\(\left(\sqrt{2}+\sqrt{3}\right)^2=2+3+2\sqrt{2\cdot3}=5+2\sqrt{6}\)
\(\left(\sqrt{5}\right)^2=5\)
Ta có \(5+2\sqrt{6}>5\)
Do đó \(\left(\sqrt{2}+\sqrt{3}\right)^2>\left(\sqrt{5}\right)^2\Leftrightarrow\sqrt{2}+\sqrt{3}>\sqrt{5}\)
2.
ĐKXĐ: \(x^2+2x-3>0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>2\\x< 1\end{matrix}\right.\)
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