$\displaystyle \begin{array}{{>{\displaystyle}l}} a)\sqrt{4x-20} +\sqrt{x-5} -\frac{1}{3}\sqrt{9x-45} =4\\ 2\sqrt{x-5} +\sqrt{x-5} -\frac{1}{3} .3\sqrt{x-5} =4\\ 2\sqrt{x-5} +\sqrt{x-5} -\sqrt{x-5} =4\\ 2\sqrt{x-5} =4\\ \rightarrow \sqrt{x-5} =2\ \\ DK\ :x\geqslant 5\ \\ Bình\ phương\ hai\ vế\ :\ x-5=4\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=9\ ( tmdk) \ \\ Vậy\ nghiệm\ pt\ là\ S=\{9\}\\ b)\sqrt{4x^{2} -4x+1} =5\ \\ \sqrt{( 2x-1)^{2}} =5\\ |2x-1|=5\\ \rightarrow \begin{cases} 2x-1=5 & \\ 2x-1=-5 & \end{cases}\rightarrow \begin{cases} x=3 & \\ x=-2 & \end{cases}\\ Tập\ nghiệm\ của\ pt\ là\ S=\{3;-2\}\\ c)\sqrt{9x^{2} +6x+1} =2x-3\\ \sqrt{( 3x+1)^{2}} =2x-3\\ |3x+1|=2x-3\\ \rightarrow \begin{cases} 3x+1=2x-3( DK\ :\ x\geqslant \frac{-1}{3} & \\ -3x-1=2x-3\left( \ x\leqslant \frac{1}{3}\right) & \end{cases}\\ \rightarrow \begin{cases} x=-4 & ( ktm)\\ x=\frac{2}{5} & ( tm) \end{cases}\\ Tập\ nghiệm\ của\ pt\ là\ S=\left\{\frac{2}{5}\right\}\\ 2.\ \\ A=2\sqrt{28} +3\sqrt{63} -5\sqrt{112} +3\sqrt{7}\\ A=4\sqrt{7} +9\sqrt{7} -20\sqrt{7} +2\sqrt{7}\\ =-5\sqrt{7} \ \\ B=( 3x-2) .\sqrt{\frac{9}{( 2-3x)^{2}}} .\ x >\frac{2}{3} \ \\ B=( 3x-2) .\frac{9}{|2-3x|} \ \\ B=( 3x-2) .\frac{9}{( 3x-2)} \ \left( \ vì\ x >\frac{2}{3}\right) \ \\ B=9\ \end{array}$
