Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ y=9\\ b.\ t=\frac{105}{16}\\ c.\ x=4\\ d.\ u=21\\ e.\ y=8\\ f.\ u=2\\ g.\ x=0;y=4;z=2 \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ \sqrt{4y-20} +\sqrt{y-5} -\frac{1}{3}\sqrt{9y-45} =4;ĐKXĐ:x\geqslant 5\\ \Leftrightarrow 2\sqrt{y-5} +\sqrt{y-5} -\sqrt{y-5} =4\\ \Leftrightarrow 2\sqrt{y-5} =4\\ \Leftrightarrow \sqrt{y-5} =2\Leftrightarrow y-5=4\Leftrightarrow y=9( tm)\\ b.\ \sqrt{t-5} +\sqrt{4t-20} -\frac{1}{5}\sqrt{9t-45} =3;ĐKXĐ:t\geqslant 5\\ \Leftrightarrow \sqrt{t-5} +2\sqrt{t-5} -\frac{3}{5}\sqrt{t-5} =3\\ \Leftrightarrow \frac{12}{5}\sqrt{t-5} =3\Leftrightarrow \sqrt{t-5} =\frac{5}{4} \Leftrightarrow t-5=\frac{25}{16}\\ \Leftrightarrow t=\frac{105}{16}( tm)\\ c.\ \sqrt{18x+9} -\sqrt{8x+4} +\frac{1}{3}\sqrt{2x+1} =4;ĐKXĐ:x\geqslant \frac{-1}{2}\\ \Leftrightarrow 3\sqrt{2x+1} -2\sqrt{2x+1} +\frac{1}{3}\sqrt{2x+1} =4\\ \Leftrightarrow \frac{4}{3}\sqrt{2x+1} =4\Leftrightarrow \sqrt{2x+1} =3\\ \Leftrightarrow 2x+1=9\Leftrightarrow x=4( tm)\\ d.\ \sqrt{4u-20} +3\sqrt{\frac{u-5}{9}} -\frac{1}{3}\sqrt{9u-45} =4;ĐKXĐ:u\geqslant 5\\ \Leftrightarrow \sqrt{u-5} +\sqrt{u-5} -\sqrt{u-5} =4\\ \Leftrightarrow \sqrt{u-5} =4\Leftrightarrow u-5=16\Leftrightarrow u=21( tm)\\ e.\ 2\sqrt{9y-27} -\frac{1}{5}\sqrt{25y-75} -\frac{1}{7}\sqrt{49y-147} =20;ĐKXĐ:y\geqslant 3\\ \Leftrightarrow 6\sqrt{y-3} -\sqrt{y-3} -\sqrt{y-3} =20\\ \Leftrightarrow 4\sqrt{y-3} =20\Leftrightarrow y-3=5\Leftrightarrow y=8( tm)\\ f.\ \frac{2}{3}\sqrt{9u-9} -\frac{1}{4}\sqrt{16u-16} +27\sqrt{\frac{u-1}{81}} =4;ĐKXĐ:u\geqslant 1\\ \Leftrightarrow 2\sqrt{u-1} -\sqrt{u-1} +3\sqrt{u-1} =4\\ \Leftrightarrow 4\sqrt{u-1} =4\Leftrightarrow u-1=1\Leftrightarrow u=2( tm)\\ g.\ \sqrt{x+1} +\sqrt{y-3} +\sqrt{z-1} =\frac{1}{2}( x+y+x) ;ĐKXĐ:x\geqslant -1;y\geqslant 3;z\geqslant 1\\ \Leftrightarrow 2\sqrt{x+1} +2\sqrt{y-3} +2\sqrt{z-1} =x+y+z\\ \Leftrightarrow \left( x+1-2\sqrt{x+1} +1\right) +\left( y-3-2\sqrt{y-3} +1\right) +\left( z-1-2\sqrt{z-1} +1\right) =0\\ \Leftrightarrow \left(\sqrt{x+1} -1\right)^{2} +\left(\sqrt{y-3} -1\right)^{2} +\left(\sqrt{z-1} -1\right)^{2} =0\\ \Leftrightarrow \sqrt{x+1} -1=0;\ \sqrt{y-3} -1=0\ và\ \sqrt{z-1} -1=0\\ \Leftrightarrow x+1=1;y-3=1;z-1=1\\ \Leftrightarrow x=0;y=4;z=2( t/m) \end{array}$
