Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 3:a.\sqrt{3} ;\ b.\ -2;\ c.\ 3;\ d.\ 2\\ Bài\ 5:\ \\ a.\ x=-2\ hoặc\ x=3\\ b.\ x=2\ hoặc\ -1\\ c.\ Không\ có\ x\ thỏa\ mãn \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 3:\\ a.\ A=\frac{1}{\sqrt{3} +1} +\frac{1}{\sqrt{3} -1} =\frac{\sqrt{3} -1+\sqrt{3} +1}{\left(\sqrt{3} +1\right) .\left(\sqrt{3} -1\right)}\\ =\frac{2\sqrt{3}}{3-1} =\sqrt{3}\\ b.\ B=\frac{1}{1-\sqrt{2}} +\frac{1}{1+\sqrt{2}} =\frac{1+\sqrt{2} +1-\sqrt{2}}{\left( 1-\sqrt{2}\right) .\left( 1+\sqrt{2}\right)}\\ =\frac{2}{1-2} =-2\\ c.\ C=\frac{5+\sqrt{5}}{5-\sqrt{5}} +\frac{5-\sqrt{5}}{5+\sqrt{5}} =\frac{\left( 5+\sqrt{5}\right)^{2} +\left( 5-\sqrt{5}\right)^{2}}{\left( 5-\sqrt{5}\right) .\left( 5+\sqrt{5}\right)}\\ =\frac{25+2\sqrt{5} +5+25-2\sqrt{5} +5}{25-5} =\frac{60}{20} =3\\ d.\ D=\frac{\sqrt{3}}{\sqrt{\sqrt{3} +1} -1} -\frac{\sqrt{3}}{\sqrt{\sqrt{3} +1} +1}\\ =\frac{\sqrt{3} .\left(\sqrt{\sqrt{3} +1} +1\right) -\sqrt{3} .\left(\sqrt{\sqrt{3} +1} -1\right)}{\left(\sqrt{\sqrt{3} +1} -1\right) .\left(\sqrt{\sqrt{3} +1} +1\right)}\\ =\frac{\sqrt{3} +\sqrt{3}}{\sqrt{3} +1-1} =\frac{2\sqrt{3}}{\sqrt{3}} =2\\ Bài\ 4:\\ a.\ VT=\sqrt{9-4\sqrt{5}} -\sqrt{5} =\sqrt{\left(\sqrt{5} -2\right)^{2}} -\sqrt{5}\\ =\sqrt{5} -2-\sqrt{5} =-2=VP\\ b.\ VT=\frac{3}{2}\sqrt{6} +2\sqrt{\frac{2}{3}} -4\sqrt{\frac{3}{2}} =\sqrt{\frac{9}{4} .6} +\sqrt{4.\frac{2}{3}} -\sqrt{16.\frac{3}{2}}\\ =\frac{3}{2}\sqrt{6} +\frac{2}{3}\sqrt{6} -2\sqrt{6} =\frac{1}{6}\sqrt{6} =\frac{\sqrt{6}}{6} =VP\\ c.\ VT=2\sqrt{2}\left(\sqrt{3} -2\right) +\left( 1+2\sqrt{2}\right)^{2} -2\sqrt{6}\\ =2\sqrt{6} -4\sqrt{2} +1+4\sqrt{2} +8-2\sqrt{6} =9=VP\\ Bài\ 5:\\ a.\ \sqrt{1-4x+4x^{2}} =5;\ ĐKXĐ:\ \forall x\\ \Leftrightarrow \sqrt{( 1-2x)^{2}} =5\\ \Leftrightarrow |1-2x|=5\\ \Leftrightarrow 1-2x=5\ hoặc\ 1-2x=-5\\ \Leftrightarrow x=-2\ hoặc\ x=3\\ b.\ \sqrt{( 2x-1)^{2}} =3;\ ĐKXĐ:\ \forall x\\ \Leftrightarrow |2x-1|=3\\ \Leftrightarrow 2x-1=3\ hoặc\ 2x-1=-3\\ \Leftrightarrow x=2\ hoặc\ -1\\ c.\ \sqrt{4-5x} =12;\ ĐKXĐ:\ x\leqslant \frac{4}{5}\\ \Leftrightarrow 4-5x =12^{2} =144\\ \Leftrightarrow x=28( loại) \end{array}$