Tìm x \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
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20 tháng 9 2023
a) \(\left(x-1\right)^3=8=2^3\)
\(x-1=2\)
\(x=2+1=3\)
b) \(7^{2x-6}=49=7^2\)
\(2x-6=2\)
\(2x=6+2=8\)
\(x=8:2=4\)
c) \(\left(2x-14\right)^7=128=2^7\)
\(2x-14=2\)
\(2x=14+2=16\)
\(x=16:2=8\)
d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)
\(x=5\)
e) \(3\cdot\left(x+2\right):7\cdot4=120\)
\(x+2=120:3\cdot7:4\)
\(x+2=70\)
\(x=70-2=68\)
AH
Akai Haruma
Giáo viên
20 tháng 9 2023
Lời giải:
a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$
$\Rightarrow x=3$
b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$
$\Rightarrow 2x=8$
$\Rightarrow x=4$
c. $(2x-14)^7=128=2^7$
$\Rightarrow 2x-14=2$
$\Rightarrow 2x=16$
$\Rightarrow x=18$
d.
$x^4.x^5=5^3.5^6$
$x^9=5^9$
$\Rightarrow x=5$
e.
$3(x+2):7=120:4=30$
$3(x+2)=30.7=210$
$x+2=210:3=70$
$x=70-2=68$
21 tháng 9 2021
\(c,\Rightarrow\left[{}\begin{matrix}-2\left(x+2\right)+\left(4-x\right)=11\left(x< -2\right)\\2\left(x+2\right)+\left(4-x\right)=11\left(-2\le x\le4\right)\\2\left(x+2\right)+\left(x-4\right)=11\left(x>4\right)\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{11}{3}\left(tm\right)\\x=3\left(tm\right)\\x=\dfrac{11}{3}\left(ktm\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{11}{3}\end{matrix}\right.\)
21 tháng 9 2021
\(a,\Rightarrow\left[{}\begin{matrix}x+\dfrac{5}{2}=3x+1\\x+\dfrac{5}{2}=-3x-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=-\dfrac{7}{8}\end{matrix}\right.\)
GN
0
LH
10
24 tháng 3 2018
\(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^8=0\)
\(\Leftrightarrow\left(2x-1\right)^6\left[1-\left(2x-1\right)^2\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(2x-1\right)^6=0\\1-\left(2x-1\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=1\\2x-1=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\2x=2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=1\end{cases}}\)
LQ
5
1 tháng 8 2018
Ta có \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Rightarrow\left(2x-1\right)^8-\left(2x-1\right)^6=0\)
\(\Rightarrow\left(2x-1\right)^6.\left[\left(2x-1\right)^2-1\right]=0\)
\(\Rightarrow\hept{\begin{cases}\left(2x-1\right)^6=0\\\left(2x-1\right)^2-1=0\end{cases}}\Rightarrow\hept{\begin{cases}2x-1=0\\\left(2x-1\right)^2=1\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{1}{2}\\\left(2x-1\right)^2=1\end{cases}}}\)
Ta có \(\left(2x-1\right)^2=1\Rightarrow\hept{\begin{cases}2x-1=1\\2x-1=-1\end{cases}\Rightarrow\hept{\begin{cases}x=1\\x=0\end{cases}}}\)
Vậy \(x\in\left\{0;\frac{1}{2};1\right\}\)
16 tháng 12 2022
1: \(\Leftrightarrow2x^2-10x-3x-2x^2=0\)
=>-13x=0
=>x=0
2: \(\Leftrightarrow5x-2x^2+2x^2-2x=13\)
=>3x=13
=>x=13/3
3: \(\Leftrightarrow4x^4-6x^3-4x^3+6x^3-2x^2=0\)
=>-2x^2=0
=>x=0
4: \(\Leftrightarrow5x^2-5x-5x^2+7x-10x+14=6\)
=>-8x=6-14=-8
=>x=1
2
16 tháng 12 2022
`1)2x(x-5)-(3x+2x^2)=0`
`<=>2x^2-10x-3x-2x^2=0`
`<=>-13x=0`
`<=>x=0`
___________________________________________________
`2)x(5-2x)+2x(x-1)=13`
`<=>5x-2x^2+2x^2-2x=13`
`<=>3x=13<=>x=13/3`
___________________________________________________
`3)2x^3(2x-3)-x^2(4x^2-6x+2)=0`
`<=>4x^4-6x^3-4x^4+6x^3-2x^2=0`
`<=>x=0`
___________________________________________________
`4)5x(x-1)-(x+2)(5x-7)=0`
`<=>5x^2-5x-5x^2+7x-10x+14=0`
`<=>-8x=-14`
`<=>x=7/4`
___________________________________________________
`5)6x^2-(2x-3)(3x+2)=1`
`<=>6x^2-6x^2-4x+9x+6=1`
`<=>5x=-5<=>x=-1`
___________________________________________________
`6)2x(1-x)+5=9-2x^2`
`<=>2x-2x^2+5=9-2x^2`
`<=>2x=4<=>x=2`
Ta có: \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
=> \(\left(2x-1\right)\in\left\{1;-1;0\right\}\)
* Nếu 2x - 1 = 1
=> 2x = 2
=> x = 2 : 2 = 1
* Nếu 2x - 1 = -1
=> 2x = (-1) + 1
=> 2x = 0
=> x = 0 : 2 = 0
* Nếu 2x - 1 = 0
=> 2x = 0 + 1
=> 2x = 1
=> x = 1 : 2
=> x = 1/2
Vậy x = { 1; 0 ; 1/2 } thì \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
CHÚC BẠN HỌC TỐT
( 2x - 1 )6 = ( 2x - 1 )8
( 2x - 1 )8 - ( 2x - 1 )6 = 0
( 2x - 1 )6 . ( ( 2x - 1 )2 - 1 ) ) = 0
Vậy ( 2x - 1 )6 = 0 hoặc ( 2x - 1 )2 - 1 = 0
2x - 1 = 0 hoặc \(\orbr{\begin{cases}2x-1=1\\2x-1=-1\end{cases}}\)
x=1/2 hoặc \(\orbr{\begin{cases}x=1\\x=0\end{cases}}\)
Vậy x \(\in\){ 1/2; 0 ;1 }