Bài giải

\(\left(2x-3\right)^6=\left(2x-3\right)^8\)

\(\left(2x-8\right)^8-\left(2x-3\right)^6=0\)

\(\left(2x-3\right)^6\left[\left(2x-3\right)^2-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(2x-3\right)^6=0\\\left(2x-3\right)^2-1=0\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}2x-3=0\\\left(2x-3\right)^2=1\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}2x=3\\2x-3=-1\text{ hoặc }2x-3=1\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=1\text{ hoặc }x=2\end{cases}}\)

\(\Rightarrow\text{ }x\in\left\{\frac{3}{2}\text{ ; }1\text{ ; }2\right\}\)

\(\left(2x-3\right)^6=\left(2x-3\right)^8\)

\(\Rightarrow\left(2x-3\right)^8-\left(2x-3\right)^6=0\)

\(\left(2x-3\right)^6\left[\left(2x-3\right)^2-1\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}\left(2x-3\right)^6=0\\\left(2x-3\right)^2-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}2x-3=0\\\left(2x-3\right)^2=1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=1;x=2\end{cases}}}\)

\(\left(x-3\right)^2\)- x+3=0

\(\left(x-3\right)^2\)-(x-3)=0

(x-3).(x-3-1)=0

(x-3).(x-4)=0

=> ta có 2 trường hợp:

th1:  x-3=0            th2: x-4=0

       => x=3             => x=4

vậy............

\(\left(x-3\right)^2-x+3=0\)

\(\left(x-3\right)^2-\left(x-3\right)=0\)

\(\left(x-3\right)\left(x-3-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}}\)

-2/5x-1/3=3/4

-2/5x=3/4+1/3

-2/5x = 13/12

x=13/12:2/5

x=-65/24

-13/20x+1/2=-2/5

-13/20x=-2/5-1/2

-13/20x=-9/10

x=-9/10:13/20

x=-18/13

4/3-|2x-1/2|=1

|2x-1/2|=1-4/3

|2x-1/2|=-1/3

<=> 2x-1/2=1/3 hoặc 2x-1/2=-1/3

TH1:

2x-1/2=1/3

2x=1/3+1/2

2x=5/6

x=5/6:2

x=5/12

TH2:

 2x-1/2=-1/3

2x=-1/3+1/2

2x=1/6

x=1/6:2

x=1/12

3 mũ 2x .(1+3²)=90

=>3 mũ 2x=9=>3 mũ 2x=3²

=>2x=2=>x=1

3^2x + 3^2x+2 = 90

=> 3^2x + 3^2x . 3² = 90

=> 3^2x . (1 + 9) = 90

=> 3^2x . 10 = 90

=> 3^2x = 9

=> 3^2x = 3²

=> 2x = 2

=> x = 1

~Std well~

1/3x=3/10-3/74

1/3x=48/185

x=144/185

\(\frac{1}{3}x+\frac{3}{74}=\frac{3}{10}\)

\(\Rightarrow\frac{1}{3}x=\frac{3}{10}-\frac{3}{74}=\frac{48}{185}\)

\(\Rightarrow x=\frac{48}{185}:\frac{1}{3}\)

\(\Rightarrow x=\frac{144}{185}\)

Bài 1:

a. 

Ta có tỉ lệ thức: 4,5 x 14,4 = 6 x 10,8

\(\Rightarrow\frac{4,5}{6}=\frac{10,8}{14,4};\frac{4,5}{10,8}=\frac{6}{14,4};\frac{6}{4,5}=\frac{14,4}{10,8};\frac{10,8}{4,5}=\frac{14,4}{6}\)

b. 

Ta có tỉ lệ thức 1: 4 x 1024 = 16 x 256

\(\Rightarrow\frac{4}{16}=\frac{256}{1024};\frac{4}{256}=\frac{16}{1024};\frac{16}{4}=\frac{1024}{256};\frac{256}{4}=\frac{1024}{16}\)

Ta có tỉ lệ thức 2: 16 x 64 = 4 x 256

\(\Rightarrow\frac{16}{4}=\frac{256}{64};\frac{16}{256}=\frac{4}{64};\frac{4}{16}=\frac{64}{256};\frac{256}{16}=\frac{64}{4}\)

Bài 2:

Áp dụng t/c DTSBN. ta có:

\(\frac{x}{11}=\frac{y}{7}=\frac{x+y}{11+7}=\frac{-54}{18}=-3\)

\(\Rightarrow x=11.\left(-3\right)=-33\)

\(\Rightarrow y=7.\left(-3\right)=-21\)

Dịch đúng rồi bạn, Toán Tiếng Anh à?

Đạt:a.m.1980=k^2

=>a.m.2³.3³.5=k²

a.m=2.3.5.l²(l là so tự nhiên)

mà:m smallest value

=>a.m=30

chọn=-30;a=-1