Bài 1:
1.
a. ĐKXĐ: $2x-1\geq 0$
$\Leftrightarrow x\geq \frac{1}{2}$
b. ĐKXĐ: \(\left\{\begin{matrix} x-1\neq 0\\ \frac{2}{x-1}\geq 0\end{matrix}\right.\Leftrightarrow x-1>0\Leftrightarrow x>1\)
2. \(\frac{1}{\sqrt{5}-2}=\frac{\sqrt{5}+2}{(\sqrt{5}-2)(\sqrt{5}+2)}=\frac{\sqrt{5}+2}{5-4}=\sqrt{5}+2\)
3.
\(\sqrt{\frac{2}{x-1}}=\frac{\sqrt{2(x-1)}}{x-1}\)
Bài 2:
a.
\(=|\sqrt{2}-\sqrt{3}|+3\sqrt{2}=\sqrt{3}-\sqrt{2}+3\sqrt{2}=\sqrt{3}+2\sqrt{2}\)
b.
\(=3\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}=\sqrt{2}(3-12+8-5)=-6\sqrt{2}\)
Bài 3: ĐKXĐ: $x\geq 1$
PT $\Leftrightarrow \sqrt{16}.\sqrt{x-1}+\sqrt{x-1}=20$
$\Leftrightarrow 4\sqrt{x-1}+\sqrt{x-1}=20$
$\Leftrightarrow 5\sqrt{x-1}=20$
$\Leftrightarrow \sqrt{x-1}=4$
$\Leftrightarrow x-1=16$
$\Leftrightarrow x=17$ (tm)
