a/ ĐKXĐ: \(x\le-\frac{3}{2}\)
\(\sqrt{2-x}+\sqrt{-3-2x}>\sqrt{7-x}\)
\(\Leftrightarrow-1-3x+2\sqrt{2x^2-x-6}>7-x\)
\(\Leftrightarrow\sqrt{2x^2-x-6}>x+4\)
\(\Leftrightarrow2x^2-x-6>x^2+8x+16\)
\(\Leftrightarrow x^2-9x-22>0\Rightarrow\left[{}\begin{matrix}x< -2\\x>11\end{matrix}\right.\)
Kếp hợp ĐKXĐ \(\Rightarrow\) \(x< -2\)
b/ ĐKXĐ: \(\left[{}\begin{matrix}x\le-1\\x\ge-\frac{2}{3}\end{matrix}\right.\)
Đặt \(3x^2+5x+2=t\ge0\)
\(\sqrt{t+5}-\sqrt{t}\ge1\)
\(\Leftrightarrow\sqrt{t+5}>\sqrt{t}+1\)
\(\Leftrightarrow t+5>t+1+2\sqrt{t}\)
\(\Leftrightarrow\sqrt{t}< 2\Rightarrow t< 4\)
\(\Leftrightarrow3x^2+5x+2< 4\)
\(\Leftrightarrow3x^2+5x-2< 0\Rightarrow-2< x< \frac{1}{3}\)
\(\Rightarrow\left[{}\begin{matrix}-2< x\le-1\\-\frac{2}{3}\le x< \frac{1}{3}\end{matrix}\right.\)
