a, TH1: \(-2\le x\le3\)
\(pt\Leftrightarrow x+2+3-x=5\)
\(\Leftrightarrow5=5\) (lđ)
=> Pt có nghiệm \(x\in\left[-2;3\right]\)
\(TH2:x\ge3\)
\(pt\Leftrightarrow x+2+x-3=5\)
\(\Leftrightarrow2x-1=5\Leftrightarrow x=3\)
\(TH3:x\le-2\)
\(pt\Leftrightarrow-x-2+3-x=5\Leftrightarrow x=-2\)
Vậy pt có nghiệm \(x\in\left[-2;3\right]\)
b, \(\left(x+1\right)\left(x+4\right)-\sqrt{x^2+5x+6}< 0\) \(\left(\left[{}\begin{matrix}x\le-3\\x\ge-2\end{matrix}\right.\right)\)
Đặt \(\sqrt{x^2+5x+6}=a\left(a\ge0\right)\)
\(pt\Leftrightarrow a^2-a-2< 0\)
\(\Leftrightarrow-1< a< 2\)
\(\Leftrightarrow0\le a\le2\)
Giair tiếp pt vs ẩn x => x...
