Tìm x biết (x-2)^8=(x-2)^6
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\(\Leftrightarrow\left(x-2\right)^8-\left(x-2\right)^6=0\\ \Leftrightarrow\left(x-2\right)^6\left[\left(x-2\right)^2-1\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-2=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\text{(x+2)(y-3)=5 }\)
\(\Rightarrow\)x+2;y-3\(\in\)Ư(5)
Mà Ư(5)={1;5;-1;-5}
Có bảng:
Th1:
x+2=1;y-3=6
=>x=-3
y=9
Tương tự 3 trường hợp còn lại
![](https://rs.olm.vn/images/avt/0.png?1311)
https://olm.vn/hoi-dap/detail/240730869813.html?pos=561319551099
Dạng giống phần a nha bạn
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1: x=3/4-1/2=3/4-2/4=1/4
2: x-1/5=2/11
=>x=2/11+1/5=21/55
3: x-5/6=16/42-8/56
=>x-5/6=8/21-4/28=5/21
=>x=5/21+5/6=15/14
4: x/5=5/6-19/30
=>x/5=25/30-19/30=6/30=1/5
=>x=1
5: =>|x|=1/3+1/4=7/12
=>x=7/12 hoặc x=-7/12
6: x=-1/2+3/4
=>x=3/4-1/2=1/4
11: x-(-6/12)=9/48
=>x+1/2=3/16
=>x=3/16-1/2=-5/16
1)x= 1/4
2)x= 2/11+ 1/5
x= 21/55
3)x - 5/6 = 5/21
x = 5/21+5/6
x = 15/14
4)x/5 = 5/6 + -19/30
x:5 = 1/5
x = 1/5.5
x = 1
5) |x| - 1/4 = 6/18
|x| = 6/18 - 1/4
|x| =7/12
⇒x= 7/12 hoặc -7/12
6)x = -1/2 +3/4
x= 1/4
7) x/15 = 3/5 + -2/3
x:15 = -1/15
x = -1/15. 15
x = -1
8)11/8 + 13/6 = 85/x
85/24 = 85/x
⇒ x = 24
9) x - 7/8 = 13/12
x = 13/12 + 7/8
x = 47/24
10)x - -6/15 = 4/27
x = 4/27 + (-6/15)
x = -34/135
11) -(-6/12)+x = 9/48
x= 9/48 - 6/12
x = -5/16
12) x - 4/6 = 5/25 + -7/15
x -4/6 = -4/15
x = -4/15 + 4/6
x = 2/5
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(6.8^{x-1}+8^{x+1}=6.8^{19}+8^{21}\)
\(\Rightarrow x-1+x+1=19+21\)
\(=2x=40\)
\(\Rightarrow x=20\)
b) \(4.3^{x-1}+2.3^{x+2}=4.3^6+2.3^9\)
\(\Rightarrow x-1+x+2=6+9\)
\(\Rightarrow2x+1=15\)
\(\Rightarrow2x=14\)
\(\Rightarrow x=7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa đề
\(\left(x-2\right)^6=\left(x-2\right)^8\)
\(\Rightarrow\left(x-2\right)^6-\left(x-2\right)^8=0\)
\(\Rightarrow\left(x-2\right)^6\left[1-\left(x-2\right)^2\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-2\right)^6=0\\1-\left(x-2\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\\left(x-2\right)^2=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0+2\\\left(x-2\right)^2=\left(\pm1\right)^2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=2\\x-2=1\\x-2=-1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=2\\x=3\\x=1\end{cases}}\)
P/s : 2 dòng cuối bn chuyển \(\hept{\begin{cases}\\\\\end{cases}}\)thành \(\orbr{\begin{cases}\\\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,x+21=6\\ \Rightarrow x=-15\\ b,x-10=-8\\ \Rightarrow x=2\\ c,\left(-8\right)x=\left(-7\right)\left(-6\right)\\ \Rightarrow\left(-8\right)x=42\\ \Rightarrow x=-4\\ d,20+8\left(x+3\right)=5^2.4\\ \Rightarrow20+8\left(x+3\right)=25.4\\ \Rightarrow20+8\left(x+3\right)=100\\ \Rightarrow8\left(x+3\right)=80\\ \Rightarrow x+3=10\\ \Rightarrow x=7\)
\(a.x+21=6\\ x=6-21\\ x=-15\\ b.x-10=-8\\ x=-8+10\\ x=2\\ c.-8x=-7.\left(-6\right)-2\\ -8x=42-2\\ -8x=40\\ x=40:\left(-8\right)\\ x=-5\)
\(d.20+8\left(x+3\right)=5^2.4\\ 20+8x+24=25.4\\ 44+8x=100\\ 8x=100-44\\ 8x=56\\ x=56:8\\ x=7\)
\(\left(x-2\right)^8=\left(x-2\right)^6\)
\(\Leftrightarrow\left(x-2\right)^8-\left(x-2\right)^6=0\)
\(\Leftrightarrow\left(x-2\right)^6.\left[\left(x-2\right)^2-1\right]=0\)
Trường hợp 1: \(\left(x-2\right)^6=0\)
\(\Leftrightarrow\left(x-2\right)^6=0^6\)
\(\Leftrightarrow x-2=0\)
\(\Leftrightarrow x=2\)
Trường hợp 2: \(\left(x-2\right)^2-1=0\)
\(\Leftrightarrow\left(x-2\right)^2=1^2\)
\(\Leftrightarrow x-2=1\)
\(\Leftrightarrow x=3\)