a: \(\sqrt{2x+3}=5\)
\(\Leftrightarrow2x+3=25\)
hay x=11
b: \(\sqrt{\left(x-2\right)^2}=8\)
\(\Leftrightarrow\left|x-2\right|=8\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.\)
a) \(\sqrt{3+2x}=5\left(đk:x\ge-\dfrac{3}{2}\right)\)
\(\Leftrightarrow3+2x=25\Leftrightarrow x=11\left(tm\right)\)
b) \(\sqrt{\left(x-2\right)^2}=8\)
\(\Leftrightarrow\left|x-2\right|=8\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.\)
c) \(đk:x\le3\)
\(\Leftrightarrow\sqrt{3-x}-3\sqrt{3-x}+5\sqrt{3-x}=6\)
\(\Leftrightarrow3\sqrt{3-x}=6\)
\(\Leftrightarrow\sqrt{3-x}=2\Leftrightarrow3-x=4\Leftrightarrow x=-1\left(tm\right)\)
d) \(đk:x\ge0\)
\(\Leftrightarrow4\sqrt{x}-6\sqrt{x}+4\sqrt{x}=5\)
\(\Leftrightarrow2\sqrt{x}=5\Leftrightarrow\sqrt{x}=\dfrac{5}{2}\Leftrightarrow x=\dfrac{25}{4}\left(tm\right)\)
e) \(đk:x\ge-5\)
\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)
\(\Leftrightarrow3\sqrt{x+5}=6\Leftrightarrow\sqrt{x+5}=2\Leftrightarrow x+5=4\Leftrightarrow x=-1\left(tm\right)\)
f) \(đk:x\ge-2\)
\(\Leftrightarrow3\sqrt{x+2}-5\sqrt{x+2}+4\sqrt{x+2}=6\)
\(\Leftrightarrow2\sqrt{x+2}=6\Leftrightarrow\sqrt{x+2}=3\Leftrightarrow x+2=9\Leftrightarrow x=7\left(tm\right)\)
a)\(\sqrt{3+2x}=5\Rightarrow3+2x=25\Rightarrow x=11\)
b)\(\sqrt{\left(x-2\right)^2}=8\Rightarrow\left|x-2\right|=8\)
\(\Rightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.\)