Bài 2:
a) \(2\sqrt{125}+\dfrac{3}{2}\sqrt{80}-\sqrt{180}-\dfrac{2}{7}\sqrt{245}\)
\(=2\sqrt{5^2\cdot5}+\dfrac{3}{2}\sqrt{4^2\cdot5}-\sqrt{6^2\cdot5}-\dfrac{2}{7}\sqrt{7^2\cdot5}\)
\(=10\sqrt{5}+\dfrac{3\cdot4}{2}\sqrt{5}-6\sqrt{5}-\dfrac{2\cdot7}{7}\sqrt{5}\)
\(=10\sqrt{5}+6\sqrt{6}-6\sqrt{5}-2\sqrt{5}\)
\(=8\sqrt{5}\)
b) \(\sqrt{11-4\sqrt{7}}-\sqrt{16+6\sqrt{7}}\)
\(=\sqrt{\left(\sqrt{7}\right)^2-2\cdot2\cdot\sqrt{7}+2^2}-\sqrt{\left(\sqrt{7}\right)^2+2\cdot3\cdot\sqrt{7}+3^2}\)
\(=\sqrt{\left(\sqrt{7}-2\right)^2}-\sqrt{\left(\sqrt{7}+3\right)^2}\)
\(=\sqrt{7}-2-\sqrt{7}-3\)
\(=-5\)
\(2a,\\ 2\sqrt{125}+\dfrac{3}{2}.\sqrt{80}-\sqrt{180}-\dfrac{2}{7}\sqrt{245}\\ =2\sqrt{5^2.5}+\dfrac{3}{2}.\sqrt{4^2.5}-\sqrt{6^2.5}-\dfrac{2}{7}.\sqrt{7^2.5}\\ =2.5.\sqrt{5}+\dfrac{3}{2}.4.\sqrt{5}-6\sqrt{5}-\dfrac{2}{7}.7\sqrt{5}\\ =10\sqrt{5}+6\sqrt{5}-6\sqrt{5}-2\sqrt{5}=8\sqrt{5}\)
3:
a: =>|x-1|=4
=>x-1=4 hoặc x-1=-4
=>x=-3 hoặc x=5
b: =>|6x-5|=4
=>6x-5=4 hoặc 6x-5=-4
=>6x=1 hoặc 6x=9
=>x=1/6 hoặc x=3/2
Bài 2:
a. $=2\sqrt{5^2.5}+\frac{3}{2}\sqrt{4^2.5}-\sqrt{6^2.5}-\frac{2}{7}\sqrt{7^2.5}$
$=2.5\sqrt{5}+\frac{3}{2}.4\sqrt{5}-6\sqrt{5}-\frac{2}{7}.7\sqrt{5}$
$=10\sqrt{5}+6\sqrt{5}-6\sqrt{5}-2\sqrt{5}$
$=10\sqrt{5}-2\sqrt{5}=8\sqrt{5}$
b.
$=\sqrt{2^2+7-2.2\sqrt{7}}-\sqrt{3^2+7+2.3\sqrt{7}}$
$=\sqrt{(2-\sqrt{7})^2}-\sqrt{(3+\sqrt{7})^2}$
$=|2-\sqrt{7}|-|3+\sqrt{7}|=\sqrt{7}-2-(3+\sqrt{7})=-5$
3)
a) \(\sqrt{\left(x-1\right)^2}=4\)
\(\Leftrightarrow\left(x-1\right)^2=4^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=4\\x-1=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)
b) \(\sqrt{36x^2-60x+25}=4\)
\(\Leftrightarrow\sqrt{\left(6x-5\right)^2}=4\)
\(\Leftrightarrow\left(6x-5\right)^2=4^2\)
\(\Leftrightarrow\left[{}\begin{matrix}6x-5=4\\6x-5=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{6}\end{matrix}\right.\)
Bài 3:
a. $\sqrt{(x-1)^2}=4$
$\Leftrightarrow |x-1|=4$
$\Leftrightarrow x-1=\pm 4$
$\Leftrightarrow x=5$ hoặc $x=-3$
b.
$\sqrt{36x^2-60x+25}=4$
$\Leftrightarrow \sqrt{(6x-5)^2}=4$
$\Leftrightarrow |6x-5|=4$
$\Leftrightarrow 6x-5=\pm 4$
$\Leftrightarrow x=\frac{3}{2}$ hoặc $x=\frac{1}{6}$
