a, ĐKXĐ : \(x\ge1\)
Ta có ; \(PT\Leftrightarrow\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}.\sqrt{9}\sqrt{x-1}+24.\sqrt{\dfrac{1}{64}}\sqrt{x-1}=-17\)
\(\Leftrightarrow\sqrt{x-1}\left(\dfrac{1}{2}-\dfrac{3}{2}\sqrt{9}+24\sqrt{\dfrac{1}{64}}\right)=-17\)
\(\Leftrightarrow-\sqrt{x-1}=-17\)
\(\Leftrightarrow\sqrt{x-1}=17\)
\(\Leftrightarrow x=290\left(TM\right)\)
Vậy ....
b, ĐKXĐ : \(x\ge3\)
Ta có : \(PT\Leftrightarrow x-3-7\sqrt{x-3}+12=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=4\\\sqrt{x-3}=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=16\\x-3=9\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=19\\x=12\end{matrix}\right.\) ( TM )
Vậy ..
a) Ta có: \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
\(\Leftrightarrow\dfrac{1}{2}\sqrt{x-1}-\dfrac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17\)
\(\Leftrightarrow-\sqrt{x-1}=-17\)
\(\Leftrightarrow x-1=17^2=289\)
hay x=290
Vậy: S={290}
b) Ta có: \(x-7\sqrt{x-3}+9=0\)
\(\Leftrightarrow x-7\sqrt{x-3}=-9\)
\(\Leftrightarrow x-3-2\cdot\sqrt{x-3}\cdot\dfrac{7}{2}+\dfrac{49}{4}=\dfrac{1}{4}\)
\(\Leftrightarrow\left(\sqrt{x-3}-\dfrac{7}{2}\right)^2=\dfrac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=4\\\sqrt{x-3}=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-3=16\\x-3=9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=19\\x=12\end{matrix}\right.\)
Vậy: S={19;12}
a \(ĐKXĐ:x\ge1\)
\(\Leftrightarrow\dfrac{1}{2}\sqrt{x-1}-\dfrac{3^2}{2}\sqrt{x-1}+\dfrac{24}{8}\sqrt{x-1}=-17\Leftrightarrow\dfrac{1}{2}-\dfrac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17\) \(\Leftrightarrow-4\sqrt{x-1}+3\sqrt{x-1}=-17\Leftrightarrow-\sqrt{x-1}=-17\Leftrightarrow\sqrt{x-1}=17\Rightarrow x-1=289\Leftrightarrow x=290\left(TM\right)\) b \(ĐKXĐ:x\ge3\)
\(\Leftrightarrow x-3-7\sqrt{x-3}+12=0\Leftrightarrow\left(\sqrt{x-3}-3\right)\left(\sqrt{x-3}-4\right)=0\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=3\\\sqrt{x-3}=4\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x-3=9\\x-3=16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\left(TM\right)\\x=19\left(TM\right)\end{matrix}\right.\)
