$\displaystyle \begin{array}{{>{\displaystyle}l}} 1.\\ a.\ \sqrt{16x^{2}} -2x+1=15\\ \Leftrightarrow |4x|-2x=14\\ TH1:\ x\geqslant 0\\ \Leftrightarrow 2x=14\Leftrightarrow x=7\ ( TM)\\ TH2:\ x< 0\\ \Leftrightarrow -6x=14\Leftrightarrow x=-\frac{7}{3} \ ( TM)\\ b.\ 3x-\sqrt{4x^{2}} -8=1\\ \Leftrightarrow 3x-|2x|=9\\ TH1:\ x\geqslant 0\\ \Leftrightarrow x=9\ ( TM)\\ TH2:\ x< 0\\ \Leftrightarrow 5x=9\Leftrightarrow x=\frac{9}{5} \ ( loại)\\ c.\ 5\sqrt{( 3x-1)^{2}} -2\sqrt{( x-1)^{2}} +3=6\\ \Leftrightarrow 5|3x-1|-2|x-1|=3\\ TH\ 1:x\geqslant 1\\ 5( 3x-1) -2( x-1) =3\\ \Leftrightarrow x=\frac{6}{13} \ ( loại)\\ TH\ 2:\ \frac{1}{3} < x< 1\\ 5( 3x-1) +2( x-1) =3\\ \Leftrightarrow x=\frac{10}{17} \ ( TM)\\ TH3:\ x\leqslant \frac{1}{3}\\ -5( 3x-1) +2( x-1) =3\\ \Leftrightarrow x=0\ ( TM)\\ d.-\sqrt{81x^{2}} -2\sqrt{( x-2)^{2}} -3=0\ ( x >1)\\ \Leftrightarrow |9x|+2|x-2|+3=0\\ TH\ 1:\ 1< x\leqslant 2:\\ 9x-2( x-2) +3=0\\ \Leftrightarrow x=-1\ ( loại)\\ TH\ 2:\ x\geqslant 2\\ 9x+2( x-2) +3=0\\ \Leftrightarrow x=\frac{1}{11} \ ( loại)\\ 2.\\ a.\ A=5\sqrt{( x-3)^{2}} -3x-5=5|x-3|-3x-5\\ TH\ 1:\ x\geqslant 3\\ A=2x-20\\ TH\ 2:\ x< 3\\ A=-8x+10\\ b.\ x=2\Rightarrow A=-8.2+10=-6\\ c.x=\sqrt{28-10\sqrt{3}} =\sqrt{\left( 5-\sqrt{3}\right)^{2}} =5-\sqrt{3} >3\\ \Rightarrow A=2\left( 5-\sqrt{3}\right) -20=-10-2\sqrt{3}\\ d.A=-3\\ TH\ 1:\ x\geqslant 3\\ A=2x-20=-3\\ \Leftrightarrow x=\frac{17}{2} \ ( TM)\\ TH\ 2:\ x< 3\\ A=-8x+10=-3\\ \Leftrightarrow x=\frac{13}{8} \ ( TM)\\ 3.\\ ĐKXD\ x\neq 1\\ a.\ B=4x-\frac{2\sqrt{( x-1)^{2}}}{1-x} +3\\ TH\ 1:\ x >1:\\ B=4x+2+3=4x+5\\ TH\ 2:\ x< 1:\\ B=4x-2+3=4x+1\\ b.\ x=\sqrt{10-2\sqrt{21}} < 1\\ \Rightarrow B=4\sqrt{10-2\sqrt{21}} +1\\ \end{array}$
