Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ A=3\sqrt{3} \ ;\ B=-5\\ Bài\ 2:\\ a.\ a\geqslant 0\ và\ a\neq 1\\ b.\ P=\frac{2}{1-\sqrt{a}}\\ c.\ P=-2\\ d.\ a=\frac{49}{81}\\ Bài\ 3:\\ a.\ x=\pm \frac{4}{3}\\ b.\ x=\sqrt{5} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a.\ A=6\sqrt{27} -2\sqrt{75} -\frac{1}{2}\sqrt{300}\\ =6.3\sqrt{3} -2.5\sqrt{3} -\frac{1}{2} .10\sqrt{3} =3\sqrt{3}\\ B=\sqrt[3]{27} -\sqrt[3]{64} -2\sqrt[3]{8}\\ =\sqrt[3]{3^{3}} -\sqrt[3]{4^{3}} -2.\sqrt[3]{2^{3}}\\ =3-4-2.2=-5\\ Bài\ 2:\\ P=\left(\frac{1}{1-\sqrt{a}} -\frac{1}{1+\sqrt{a}}\right) .\left(\frac{1}{\sqrt{a}} +1\right)\\ a.\ ĐKXĐ:\ a\geqslant 0\ và\ a\neq 1\\ b.\ P=\frac{1+\sqrt{a} -1+\sqrt{a}}{\left( 1+\sqrt{a}\right)\left( 1-\sqrt{a}\right)} .\frac{1+\sqrt{a}}{\sqrt{a}} =\frac{2}{1-\sqrt{a}}\\ c.\ Khi\ a=4\ thì\ P=\frac{2}{1-\sqrt{4}} =-2\\ d.\ P=9\Leftrightarrow \frac{2}{1-\sqrt{a}} =9\Leftrightarrow 9-9\sqrt{a} =2\\ \Leftrightarrow 9\sqrt{a} =7\Leftrightarrow \sqrt{a} =\frac{7}{9} \Leftrightarrow a=\frac{49}{81}\\ Bài\ 3:\\ a.\ \sqrt{9x^{2}} =4\Leftrightarrow |3x|=4\Leftrightarrow 3x=\pm 4\Leftrightarrow x=\pm \frac{4}{3}\\ b.\ x^{2} -2\sqrt{5} x+5=0\Leftrightarrow \left( x-\sqrt{5}\right)^{2} =0\\ \Leftrightarrow x-\sqrt{5} =0\Leftrightarrow x=\sqrt{5} \end{array}$
