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43.
ĐKXĐ: \(\left[{}\begin{matrix}x\le-1\\x\ge5\end{matrix}\right.\)
\(2\left(x^2-4x-5\right)-3\sqrt{x^2-4x-5}-2=0\)
Đặt \(\sqrt{x^2-4x-5}=u\ge0\)
\(\Rightarrow2u^2-3u-2=0\)
\(\Rightarrow\left[{}\begin{matrix}u=2\\u=-\dfrac{1}{2}\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x^2-4x-5}=2\)
\(\Rightarrow x^2-4x-5=4\)
\(\Leftrightarrow x^2-4x-9=0\) (bấm máy, nghiệm luôn thỏa mãn)
44.
ĐKXĐ:
A.
\(x^2+x+2\ge0\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{7}{4}\ge0\) (luôn đúng)
\(\Rightarrow x\in R\)
B.
\(1-3x>0\Rightarrow x< \dfrac{1}{3}\)
C.
\(1-9x^2\ge0\Rightarrow x^2\le\dfrac{1}{9}\)
\(\Rightarrow-\dfrac{1}{3}\le x\le\dfrac{1}{3}\)
D.
\(x^2-5x+6>0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)>0\)
\(\Rightarrow\left[{}\begin{matrix}x>3\\x< 2\end{matrix}\right.\)
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