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YN
14 tháng 9 2021
Đề yêu cầu tìm x ặ?
\(\left(x+2\right)\left(3x-1\right)+\left(x-1\right)\left(2-3x\right)=6\)
\(\Rightarrow3x^2-x+6x-2+2x-3x^2-2+3x=6\)
\(\Rightarrow\left(3x^2-3x^2\right)+\left(-x+6x+2x+3x\right)+\left(-2-2\right)=6\)
\(\Rightarrow10x-4=6\)
\(\Rightarrow10x=10\)
\(\Rightarrow x=1\)
8 tháng 3 2022
a: =>(3x+1)(3x-1)-(3x+1)(2x-3)=0
=>(3x+1)(3x-1-2x+3)=0
=>(3x+1)(x+2)=0
=>x=-1/3 hoặc x=-2
b: =>(3x+1)(6x+2)-(3x+1)(x-2)=0
=>(3x+1)(6x+2-x+2)=0
=>(3x+1)(5x+4)=0
=>x=-1/3 hoặc x=-4/5
17 tháng 1 2023
\(1,\dfrac{4x-3}{x-5}=\dfrac{29}{3}\left(ĐKXĐ:x\ne5\right)\)
\(\Rightarrow3\left(4x-3\right)=29\left(x-5\right)\)
\(\Leftrightarrow12x-9=29x-145\)
\(\Leftrightarrow12x-9-29x+145=0\)
\(\Leftrightarrow-17x+136=0\)
\(\Leftrightarrow-17x=-136\)
\(\Leftrightarrow x=8\left(tm\right)\)
Vậy \(S=\left\{8\right\}\)
\(2,\dfrac{2x-1}{5-3x}=2\left(ĐKXĐ:x\ne\dfrac{5}{3}\right)\)
\(\Rightarrow2x-1=2\left(5-3x\right)\)
\(\Leftrightarrow2x-1=10-6x\)
\(\Leftrightarrow2x-1-10+6x=0\)
\(\Leftrightarrow8x-11=0\)
\(\Leftrightarrow8x=11\)
\(\Leftrightarrow x=\dfrac{11}{8}\left(tm\right)\)
Vậy \(S=\left\{\dfrac{11}{8}\right\}\)
\(3,\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\left(ĐKXĐ:x\ne1\right)\)
\(\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\)
\(\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2x-2}{x-1}+\dfrac{x}{x-1}\)
\(\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{3x-2}{x-1}\)
\(\Rightarrow4x-5=3x-2\)
\(\Leftrightarrow4x-5-3x+2=0\)
\(\Leftrightarrow x-3=0\)
\(\Leftrightarrow x=3\left(tm\right)\)
Vậy \(S=\left\{3\right\}\)
\(4,\dfrac{2x+5}{2x}-\dfrac{x}{x+5}=0\left(ĐKXĐ:x\ne\dfrac{1}{2};x\ne-5\right)\)
\(\Leftrightarrow\dfrac{\left(2x+5\right)\left(x+5\right)}{2x\left(x+5\right)}-\dfrac{2x^2}{2x\left(x+5\right)}=0\)
\(\Leftrightarrow\dfrac{2x^2+15x+25}{2x\left(x+5\right)}-\dfrac{2x^2}{2x\left(x+5\right)}=0\)
\(\Leftrightarrow\dfrac{15x+25}{2x\left(x+5\right)}=0\)
\(\Rightarrow15x+25=0\)
\(\Leftrightarrow15x=-25\)
\(\Leftrightarrow x=\dfrac{-5}{3}\left(tm\right)\)
Vậy \(S=\left\{\dfrac{-5}{3}\right\}\)
Y
17 tháng 1 2023
\(1,\dfrac{4x-3}{x-5}=\dfrac{29}{3}\)
\(\Leftrightarrow\dfrac{3\left(4x-3\right)-29\left(x-5\right)}{3\left(x-5\right)}=0\)
\(\Leftrightarrow12x-9-29x+145=0\)
\(\Leftrightarrow-17x=-136\)
\(\Leftrightarrow x=8\)
\(2,\dfrac{2x-1}{5-3x}=2\)
\(\Leftrightarrow\dfrac{2x-1-2\left(5-3x\right)}{5-3x}=0\)
\(\Leftrightarrow2x-1-10+6x=0\)
\(\Leftrightarrow8x=11\)
\(\Leftrightarrow x=\dfrac{11}{8}\)
\(3,\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)
\(\Leftrightarrow\dfrac{4x-5-2\left(x-1-x\right)}{x-1}=0\)
\(\Leftrightarrow4x-5-2x+2+2x=0\)
\(\Leftrightarrow4x=3\)
\(\Leftrightarrow x=\dfrac{3}{4}\)
\(4,\dfrac{2x+5}{2x}-\dfrac{x}{x+5}=0\)
\(\Leftrightarrow\dfrac{\left(2x+5\right)\left(x+5\right)-2x^2}{2x\left(x+5\right)}=0\)
\(\Leftrightarrow2x^2+10x+5x+25-2x^2=0\)
\(\Leftrightarrow15x=-25\)
\(\Leftrightarrow x=-\dfrac{5}{3}\)
2 tháng 4 2022
a: (3x-2)(4x+5)=0
=>3x-2=0 hoặc 4x+5=0
=>x=2/3 hoặc x=-5/4
b: (2,3x-6,9)(0,1x+2)=0
=>2,3x-6,9=0 hoặc 0,1x+2=0
=>x=3 hoặc x=-20
c: =>(x-3)(2x+5)=0
=>x-3=0 hoặc 2x+5=0
=>x=3 hoặc x=-5/2
TN
1 tháng 4 2016
(3x-2)(4x-5)=0
Th1:3x-2=0
=>3x=2
=>x=\(\frac{2}{3}\)
Th2:4x-5=0
=>4x=5
=>x=\(\frac{5}{4}\)
vậy x=...
17 tháng 5 2021
`x^2+2x+3>2`
`<=>x^2+2x+1>0`
`<=>(x+1)^2>0`
`<=>x+1 ne 0`
`<=>x ne -1`
`(x+5)(3x^2+2)>0`
Vì `3x^2+2>=2>0`
`=>x+5>0<=>x>-5`
17 tháng 5 2021
c) Ta có: \(21x-10x^2+9< 0\)
\(\Leftrightarrow10x^2-21x-9>0\)
\(\Leftrightarrow x^2-\dfrac{21}{10}x-\dfrac{9}{10}>0\)
\(\Leftrightarrow x^2-2\cdot x\cdot\dfrac{21}{20}+\dfrac{441}{400}>\dfrac{801}{400}\)
\(\Leftrightarrow\left(x-\dfrac{21}{20}\right)^2>\dfrac{801}{400}\)
\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{3\sqrt{89}+21}{20}\\x< \dfrac{-3\sqrt{89}+21}{20}\end{matrix}\right.\)
Ta có : 3x2 - 6x = 0
=> 3x(x - 2) = 0
\(\Leftrightarrow\orbr{\begin{cases}3x=0\\x-2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)