\(a.\sqrt{2x-3}=5\\ \Rightarrow2x-3=5^2\\ \Leftrightarrow2x-3=25\\ \Leftrightarrow2x=28\\ \Leftrightarrow x=14\)
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\(b.\sqrt{3-4x}=7\\ \Leftrightarrow3-4x=7^2\\ \Leftrightarrow3-4x=49\\ \Leftrightarrow-4x=-46\\ x=\dfrac{23}{2}\)
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\(c.\sqrt{x^2+1}=5\\ \Rightarrow x^2+1=25\\ \Leftrightarrow x^2=24\\ \Leftrightarrow\left[{}\begin{matrix}x=\sqrt{24}\\x=-\sqrt{24}\end{matrix}\right.\)
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\(d.\sqrt{4x+5}=2\\ \Rightarrow4x+5=4\\ \Leftrightarrow4x=-1\\ \Leftrightarrow x=\dfrac{-1}{4}\)
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\(e.\sqrt{\dfrac{3x-1}{2-x}}=\dfrac{1}{2}\left(ĐKXĐ:x>2\right)\\ \Rightarrow\dfrac{3x-1}{2-x}=\dfrac{1}{4}\\ \Leftrightarrow\dfrac{4\left(3x-1\right)}{4\left(2-x\right)}=\dfrac{2-x}{4\left(2-x\right)}\\ \Leftrightarrow\dfrac{12x-4-2+x}{4\left(2-x\right)}=0\\ \Rightarrow12x-4-2+x=0\\ \Leftrightarrow13x-6=0\\ \Leftrightarrow13x=6\\ \Leftrightarrow x=\dfrac{6}{13}\)
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\(f.\sqrt{\dfrac{x+1}{x-2}}=\dfrac{2}{3}\left(ĐKXĐ:x>2\right)\\ \Rightarrow\dfrac{x+1}{x-2}=\dfrac{4}{9}\\ \Leftrightarrow\dfrac{9\left(x+1\right)}{9\left(x-2\right)}=\dfrac{4\left(x-2\right)}{9\left(x-2\right)}\\ \Rightarrow9x+9-4x+8=0\\ \Leftrightarrow5x+17=0\\ \Leftrightarrow x=\dfrac{-17}{5}\)
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