a: \(\Leftrightarrow3\sqrt{x-5}-2\sqrt{x-5}+\dfrac{1}{4}\cdot2\sqrt{x-5}=3\)
=>\(\dfrac{3}{2}\sqrt{x-5}=3\)
=>x-5=4
=>x=9
b: \(\Leftrightarrow\sqrt{2x-1}=2x-7\)
=>2x-1=4x^2-28x+49 và x>=7/2
=>4x^2-28x+49-2x+1=0 va x>=7/2
=>4x^2-30x+50=0 và x>=7/2
=>x=5
\(a,ĐKXĐ:x\ge5\\ \sqrt{9x-45}-14\sqrt{\dfrac{x-5}{49}}+\dfrac{1}{4}\sqrt{4x-20}=3\\ \Leftrightarrow\sqrt{9\left(x-5\right)}-14.\dfrac{\sqrt{x-5}}{\sqrt{49}}+\dfrac{1}{4}\sqrt{4\left(x-5\right)}=3\\ \Leftrightarrow\sqrt{9}.\sqrt{x-5}-14.\dfrac{\sqrt{x-5}}{7}+\dfrac{1}{4}.\sqrt{4}\sqrt{x-5}=3\\ \Leftrightarrow3\sqrt{x-5}-2\sqrt{x-5}+\dfrac{1}{4}.2\sqrt{x-5}=3\\ \Leftrightarrow\sqrt{x-5}+\dfrac{1}{2}\sqrt{x-5}=3\\ \Leftrightarrow\dfrac{3}{2}\sqrt{x-5}=3\\ \Leftrightarrow\sqrt{x-5}=2\\ \Leftrightarrow x-5=4\\ \Leftrightarrow x=9\left(tm\right)\)
\(b,ĐKXĐ:x\ge\dfrac{1}{2}\\ 2x=\sqrt{2x-1}+7\\ \Leftrightarrow2x-7-\sqrt{2x-1}=0\\ \Leftrightarrow2x-1-\sqrt{2x-1}-6=0\\ \Leftrightarrow2x-1-3\sqrt{2x-1}+2\sqrt{2x-1}-6=0\\ \Leftrightarrow\sqrt{2x-1}\left(\sqrt{2x-1}-3\right)+2\left(\sqrt{2x-1}-3\right)=0\\ \Leftrightarrow\left(\sqrt{2x-1}-3\right)\left(\sqrt{2x-1}+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{2x-1}-3=0\\\sqrt{2x-1}+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{2x-1}=3\\\sqrt{2x-1}=-2\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow2x-1=9\\ \Leftrightarrow2x=10\\ \Leftrightarrow x=5\left(tm\right)\)
