Đáp án:

$\begin{array}{l}
1)a)24.161 = 84.46\\
\left\{ \begin{array}{l}
\dfrac{{24}}{{84}} = \dfrac{{46}}{{161}};\dfrac{{24}}{{46}} = \dfrac{{84}}{{161}}\\
\dfrac{{161}}{{84}} = \dfrac{{46}}{{24}};\dfrac{{161}}{{46}} = \dfrac{{84}}{{24}}
\end{array} \right.\\
b)2.3 = 1.6\\
 \Rightarrow \dfrac{2}{1} = \dfrac{6}{3};\dfrac{2}{6} = \dfrac{1}{3};\dfrac{6}{2} = \dfrac{3}{1};\dfrac{3}{6} = \dfrac{1}{2}\\
2)a)\dfrac{x}{{27}} = \dfrac{{ - 2}}{{3,6}}\\
 \Rightarrow x.3,6 = 27.\left( { - 2} \right) =  - 54\\
 \Rightarrow x =  - 54:3,6\\
 \Rightarrow x =  - 15\\
Vay\,x =  - 15\\
b)\dfrac{x}{{15}} = \dfrac{{60}}{x}\\
 \Rightarrow {x^2} = 60.15 = 900\\
 \Rightarrow \left[ \begin{array}{l}
x = 30\\
x =  - 30
\end{array} \right.\\
c){\left( {4x + 5} \right)^2} = 9\\
 \Rightarrow \left[ \begin{array}{l}
4x + 5 = 3\\
4x + 5 =  - 3
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
4x =  - 2\\
4x =  - 8
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x =  - \dfrac{1}{2}\\
x =  - 2
\end{array} \right.\\
d){\left( {5x - 3} \right)^3} =  - 25\\
 \Rightarrow 5x - 3 =  - \sqrt[3]{{25}}\\
 \Rightarrow x = \dfrac{{ - \sqrt[3]{{25}} + 3}}{5}\\
NC:\dfrac{x}{2} = \dfrac{y}{5} = k\\
 \Rightarrow \left\{ \begin{array}{l}
x = 2k\\
y = 5k
\end{array} \right.\\
x.y = 90\\
 \Rightarrow 2k.5k = 90\\
 \Rightarrow {k^2} = 9\\
 \Rightarrow \left[ \begin{array}{l}
k = 3\\
k =  - 3
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = 6;y = 15\\
x =  - 6;y =  - 15
\end{array} \right.
\end{array}$

1.

 a)24/84=161/46                            b)2/1=3/6

    24/161=84/46                               2/3=1/6

    46/161=84/24                               6/1=3/2

    46/84=161/24                               6/3=1/2

2.

a)x/27=-2/3,6                                 b)x/15=60/x

=>x.3,6=27.(-2)                              =>x.x=15.60

=>x.3,6=-54                                   =>x^2=900

=>x=-54:3,6                                   =>x=30 hoặc x=-30

=>x=15                                          

c)(4x+5)^2=9                                 d)Ýd của bạn hình như là chép sai đề bài hay 

=>(4x+5)^2=3^2                             sao ý

=>4x+5=3

=>4x=3-5

=>4x=-2

=>x=-2:4

=>x=-2/4

NC

Ta có: x/2=y/5=x/2.x/2=y/5.x/2=y/5.y/5

=>x^2/4=y^2/25=xy/10=90/10=9

=>x^2/4=9=>x^2=36=>x=+6;-6

     y^2/25=9=>y^2=225=>y=+15;-15

=>(x,y)=(+6;+15);(-6;-15)