Bài 1:
a: \(\sqrt{\left(3-2\sqrt3\right)^2}+\sqrt{\left(3+2\sqrt3\right)^2}\)
\(=2\sqrt3-3+2\sqrt3+3\)
\(=4\sqrt3\)
b: \(\sqrt{\left(6-3\sqrt6\right)^2}-\sqrt{\left(6+3\sqrt6\right)^2}\)
\(=\left|6-3\sqrt6\right|-\left(6+3\sqrt6\right)\)
\(=3\sqrt6-6-6-3\sqrt6=-12\)
c: \(\sqrt{\left(2-\sqrt3\right)^2}+\sqrt{\left(1-\sqrt3\right)^2}\)
\(=\left|2-\sqrt3\right|+\left|\sqrt3-1\right|\)
\(=2-\sqrt3+\sqrt3-1=2-1=1\)
d: \(\sqrt{\left(3+\sqrt2\right)^2}-\sqrt{\left(1-\sqrt2\right)^2}\)
\(=3+\sqrt2-\left(\sqrt2-1\right)\)
\(=3+\sqrt2-\sqrt2+1=4\)
e: \(\sqrt{\left(\sqrt5-\sqrt2\right)^2}+\sqrt{\left(\sqrt5+\sqrt2\right)^2}\)
\(=\sqrt5-\sqrt2+\sqrt5+\sqrt2=2\sqrt5\)
f: \(\sqrt{\left(\sqrt2+1\right)^2}-\sqrt{\left(2\sqrt2-4\right)^2}\)
\(=\sqrt2+1-\left|4-2\sqrt2\right|\)
\(=\sqrt2+1-\left(4-2\sqrt2\right)=\sqrt2+1-4+2\sqrt2=3\sqrt2-3\)
Bài 2:
a: ĐKXĐ: 1-2x>=0
=>2x<=1
=>\(x\le\frac12\)
b: ĐKXĐ: \(\begin{cases}2x+3\ge0\\ x-1<>0\end{cases}\)
=>x>=-3/2 và x<>1
c: ĐKXĐ: \(\begin{cases}1-4x\ge0\\ x^2-1<>0\end{cases}\Rightarrow\begin{cases}4x\le1\\ x^2<>1\end{cases}\)
=>\(\begin{cases}x<=\frac14\\ x<>-1\end{cases}\)
d: ĐKXĐ: \(\frac{-1}{4x-3}\ge0\)
=>4x-3<0
=>4x<3
=>x<3/4
