a) \(4\sqrt{x}-2\sqrt{9x}+\sqrt{16x}=5\)
\(\Leftrightarrow4\sqrt{x}-6\sqrt{x}+4\sqrt{x}=5\)
\(\Leftrightarrow2\sqrt{x}=5\)
\(\Leftrightarrow\sqrt{x}=\dfrac{5}{2}\)
\(\Leftrightarrow x=\left(\dfrac{5}{2}\right)^2=\dfrac{25}{4}\)
b) \(\sqrt{x^2-9}-\sqrt{4x-12}=0\)
\(\Leftrightarrow\sqrt{\left(x+3\right)\left(x-3\right)}-2\sqrt{x-3}=0\)
\(\Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=0\\\sqrt{x+3}-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\\sqrt{x-3}=2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x-3=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=7\end{matrix}\right.\)
c) \(\sqrt{x^2-\dfrac{1}{2}x+\dfrac{1}{16}}=1\)
\(\Leftrightarrow\sqrt{\left(x-\dfrac{1}{4}\right)^2}=1\)
\(\Leftrightarrow\left|x-\dfrac{1}{4}\right|=1\)
TH1: \(\left|x-\dfrac{1}{4}\right|=x-\dfrac{1}{4}\) với \(x-\dfrac{1}{4}\ge0\Leftrightarrow x\ge\dfrac{1}{4}\)
Pt trở thành:
\(x-\dfrac{1}{4}=1\) (ĐK: \(x\ge\dfrac{1}{4}\))
\(\Leftrightarrow x=\dfrac{5}{4}\) (tm)
TH2: \(\left|x-\dfrac{1}{4}\right|=-\left(x-\dfrac{1}{4}\right)\) với \(x-\dfrac{1}{4}< 0\Leftrightarrow x< \dfrac{1}{4}\)
Pt trở thành:
\(-\left(x-\dfrac{1}{4}\right)=1\) (ĐK: \(x< \dfrac{1}{4}\) )
\(\Leftrightarrow-x+\dfrac{1}{4}=1\)
\(\Leftrightarrow x=\dfrac{1}{4}-1=-\dfrac{3}{4}\) (tm)
a: =>4căn x-6căn x+4căn x=5
=>2*căn x=5
=>căn x=5/2
=>x=25/4
b: =>\(\sqrt{x-3}\left(\sqrt{x+3}-2\right)=0\)
=>x-3=0 hoặc x+3=4
=>x=1 hoặc x=3
c: =>|x-1/4|=1
=>x-1/4=1 hoặc x-1/4=-1
=>x=3/4 hoặc x=5/4
