16) ĐKXĐ: \(x\ge-\dfrac{1}{4}\)
\(\sqrt{4x+1}-\sqrt{3x+4}=1\\ \Leftrightarrow\sqrt{4x+1}=1+\sqrt{3x+4}\\ \Rightarrow4x+1=1+3x+4+2\sqrt{3x+4}\\ \Leftrightarrow x-4=2\sqrt{3x+4}\\ \Leftrightarrow x^2-8x+16=12x+16\\ \Leftrightarrow x^2-20x=0\\ \Leftrightarrow x\left(x-20\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=20\end{matrix}\right.\)
Thử lại \(x=0\) không thỏa mãn \(\Rightarrow x=20\)
\(16,ĐK:x\ge-\dfrac{1}{4}\\ PT\Leftrightarrow\sqrt{4x+1}=\sqrt{3x+4}+1\\ \Leftrightarrow4x+1=3x+4+1+2\sqrt{3x+4}\\ \Leftrightarrow x-4=2\sqrt{3x+4}\\ \Leftrightarrow x^2-8x+16=12x+16\\ \Leftrightarrow x^2-20x=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=20\left(tm\right)\end{matrix}\right.\)
\(17,ĐK:x\ge2\\ PT\Leftrightarrow2x+2\sqrt{\left(x+2\sqrt{2x-4}\right)\left(x-2\sqrt{2x-4}\right)}=8\\ \Leftrightarrow4-x=\sqrt{x^2-4\left(2x-4\right)}\\ \Leftrightarrow\sqrt{x^2-8x+16}=4-x\\ \Leftrightarrow\left|x-4\right|=4-x\\ \Leftrightarrow\left[{}\begin{matrix}x-4=4-x\left(x\ge4\right)\\4-x=4-x\left(2\le x< 4\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)
