$\displaystyle \begin{array}{{>{\displaystyle}l}} a)\sqrt{9x+27} +5\sqrt{x+3} -\frac{3}{4}\sqrt{16x+48} =5\\ \rightarrow 3\sqrt{x+3} +5\sqrt{x+3} -\frac{3}{4} .4\sqrt{x+3} =5\\ \rightarrow 3\sqrt{x+3} +5\sqrt{x+3} -3\sqrt{x+3} =5\\ \rightarrow 5\sqrt{x+3} =5\ \\ DK\ :x\geqslant -3\ \\ \rightarrow \sqrt{x+3} =1\\ \rightarrow x+3=1\\ \rightarrow x=-2( \ tmdk) \ \\ Vậy..............\ \\ b)\sqrt{49x-98} -14\sqrt{\frac{x-2}{49}} =3\sqrt{x-2} +8\\ \rightarrow 7\sqrt{x-2} -14.\frac{\sqrt{x-2}}{7} -3\sqrt{x-2} =8\\ \rightarrow 7\sqrt{x-2} -2\sqrt{x-2} -3\sqrt{x-2} =8\\ \rightarrow 2\sqrt{x-2} =8\\ \rightarrow \sqrt{x-2} =4\\ Dk\ :x\geqslant 2\\ \rightarrow x-2=16\\ \rightarrow x=18( tmdk) \ \\ Vậy...................\ \\ c)\sqrt{x+1} -\sqrt{x-2} =1\ \\ DK\ :x\geqslant 2\ \\ \rightarrow \left(\sqrt{x+1} -\sqrt{x-2}\right)^{2} =1\\ \rightarrow x+1+x-2-2\sqrt{( x-1)( x-2)} =1\\ \rightarrow 2x-1-2\sqrt{( x-1)( x-2)} =1\\ \rightarrow 2( x-1) -2\sqrt{( x-1)( x-2)} =0\ \\ \rightarrow 2\sqrt{x-1}\left(\sqrt{x-1} -\sqrt{x-2}\right) =0\ \\ \rightarrow \left[ \begin{array}{l l} x-1=0 & \\ \sqrt{x-1} -\sqrt{x-2} =0 & \end{array} \right.\rightarrow \left[ \begin{array}{l l} x=1( ktm) & \\ \sqrt{x-1} =\sqrt{x-2} & ( vô\ lí) \ \end{array} \right.\\ do\ đó\ pt\ vô\ nghiệm\ \\ d)\sqrt{x^{2} +1} +\sqrt{4x^{2} -4x+5} =0\ \\ \sqrt{x^{2} +1} +\sqrt{( 2x-1)^{2} +4} =0\ ( 1)\\ Ta\ có\ :\ \sqrt{x^{2} +1} >0\ với\ mọi\ x\ \\ \sqrt{( 2x-1)^{2} +4} >0\ với\ mọi\ x\ \\ do\ đó\ ( 1) \ vô\ nghiệm\ \end{array}$