Giải phương trình
\(|3x+1-3=x|\)
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Y
12 tháng 4 2022
\(a,\dfrac{x-3}{x}=\dfrac{x-3}{x+3}\)\(\left(đk:x\ne0,-3\right)\)
\(\Leftrightarrow\dfrac{x-3}{x}-\dfrac{x-3}{x+3}=0\)
\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+3\right)-x\left(x-3\right)}{x\left(x+3\right)}=0\)
\(\Leftrightarrow x^2-9-x^2+3x=0\)
\(\Leftrightarrow3x-9=0\)
\(\Leftrightarrow3x=9\)
\(\Leftrightarrow x=3\left(n\right)\)
Vậy \(S=\left\{3\right\}\)
Y
12 tháng 4 2022
\(b,\dfrac{4x-3}{4}>\dfrac{3x-5}{3}-\dfrac{2x-7}{12}\)
\(\Leftrightarrow\dfrac{4x-3}{4}-\dfrac{3x-5}{3}+\dfrac{2x-7}{12}>0\)
\(\Leftrightarrow\dfrac{3\left(4x-3\right)-4\left(3x-5\right)+2x-7}{12}>0\)
\(\Leftrightarrow12x-9-12x+20+2x-7>0\)
\(\Leftrightarrow2x+4>0\)
\(\Leftrightarrow2x>-4\)
\(\Leftrightarrow x>-2\)
1 tháng 7 2017
Ta có : 17 - 14(x + 1) = 13 - 4(x + 1) - 5(x - 3)
<=> 17 - 14x - 14 = 13 - 4x - 4 - 5x + 15
<=> -14x + 3 = -9x + 24
<=> -14x + 9x = 24 - 3
<=> -5x = 21
=> x = -4,2
1 tháng 7 2017
Ta có : 5x + 3,5 + (3x - 4) = 7x - 3(x - 0,5)
<=> 5x + 3,5 + 3x - 4 = 7x - 3x + 1,5
<=> 8x - 0,5 = 4x + 1,5
=> 8x - 4x = 1,5 + 0,5
=> 4x = 2
=> x = \(\frac{1}{2}\)
22 tháng 7 2021
1) Ta có: \(4x+8=3x-1\)
\(\Leftrightarrow4x-3x=-1-8\)
\(\Leftrightarrow x=-9\)
2) Ta có: \(10-5\left(x+3\right)>3\left(x-1\right)\)
\(\Leftrightarrow10-5x-15-3x+3>0\)
\(\Leftrightarrow-8x>2\)
hay \(x< \dfrac{-1}{4}\)
9 tháng 2 2021
PT \(\Leftrightarrow9x^2-6x+1-9x+6=9x^2-18x-27\)
\(\Leftrightarrow9x^2-6x+1-9x+6-9x^2+18x+27=0\)
\(\Leftrightarrow3x+34=0\)
\(\Leftrightarrow x=-\dfrac{34}{3}\)
Vậy ...
9 tháng 2 2021
Ta có: \(\left(3x-1\right)^2-3\left(3x-2\right)=9\left(x+1\right)\left(x-3\right)\)
\(\Leftrightarrow9x^2-6x+1-9x+6=9\left(x^2-3x+x-3\right)\)
\(\Leftrightarrow9x^2-15x+7=9x^2-18x-27\)
\(\Leftrightarrow9x^2-15x+7-9x^2+18x+27=0\)
\(\Leftrightarrow3x+34=0\)
\(\Leftrightarrow3x=-34\)
\(\Leftrightarrow x=-\dfrac{34}{3}\)
Vậy: \(S=\left\{-\dfrac{34}{3}\right\}\)
C
1
20 tháng 6 2023
=>\(\dfrac{3x^3-9x^2+9x-2x^3+2x^2-6x}{\left(x^2-3x+3\right)\left(x^2-x+3\right)}=-1\)
=>x^3-7x^2+3x=-[(x^2+3)^2-4x(x^2+3)+3x^2]
=>x^3-7x^2+3x+(x^2+3)^2-4x(x^2+3)+3x^2=0
=>x^3-4x^2+3x+x^4+6x^2+9-4x^3-12x=0
=>x^4-3x^3+2x^2-9x+9=0
=>(x-3)(x-1)(x^2+x+3)=0
=>x=3;x=1
2N
1
TM
22 tháng 5 2022
\(\dfrac{3x}{x^2-x+3}-\dfrac{2x}{x^2-3x+3}+1=0\left(a\right)\)
Ta có : \(x^2-x+3=x^2-x+\dfrac{1}{4}+\dfrac{11}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{11}{4}>0\)
\(x^2-3x+3=x^2-3x+\dfrac{9}{4}+\dfrac{3}{4}=\left(x-\dfrac{3}{2}\right)^2+\dfrac{3}{4}>0\)
\(\RightarrowĐKXĐ:x\in R\)
Đặt : \(t=x^2-x+3\)
\(\left(a\right)\Leftrightarrow\dfrac{3x}{t}-\dfrac{2x}{t-2x}+1=0\)
\(\Leftrightarrow3x\left(t-2x\right)-2xt+t\left(t-2x\right)=0\)
\(\Leftrightarrow t^2-xt-6x^2=0\)
\(\Leftrightarrow t^2+2xt-3xt-6x^2=0\)
\(\Leftrightarrow t\left(t+2x\right)-3x\left(t+2x\right)=0\)
\(\Leftrightarrow\left(t-3x\right)\left(t+2x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t-3x=0\\t+2x=0\end{matrix}\right.\left(b\right)\)
Thay \(t=x^2-x+3\) lại vào (b) được :
\(\left[{}\begin{matrix}x^2-x+3-3x=0\\x^2-x+3+2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2-4x+3=0\\x^2+x+3=0\end{matrix}\right.\left(c\right)\)
Mà : \(x^2-4x+3=x^2-x-3x+3\)
\(=x\left(x-1\right)-3\left(x-1\right)=\left(x-1\right)\left(x-3\right)\left(c'\right)\)
và : \(x^2+x+3=x^2+x+\dfrac{1}{4}+\dfrac{11}{4}\)
\(=\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\left(c''\right)\)
Thay (c') và (c'') vào (c) được :
\(\left[{}\begin{matrix}\left(x-1\right)\left(x-3\right)=0\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x-1=0\Leftrightarrow x=1\left(tmđk\right)\\x-3=0\Leftrightarrow x=3\left(tmđk\right)\end{matrix}\right.\\\left(x+\dfrac{1}{2}\right)^2=-\dfrac{11}{4}\Leftrightarrow x\in\varnothing\end{matrix}\right.\)
Vậy : Phương trình có tập nghiệm \(S=\left\{1;3\right\}\)
20 tháng 3 2023
a: =>x(x+3)=0
=>x=0 hoặc x=-3
b: =>x(1-2x)=0
=>x=0 hoặc x=1/2
c: =>(x-7)(2x+3-x)=0
=>(x-7)(x+3)=0
=>x=7 hoặc x=-3
d: =>(x-2)(3x-1-x-3)=0
=>(x-2)(2x-4)=0
=>x=2
NH
20 tháng 3 2023
a)
`x^2 +3x=0`
`<=>x(x+3)=0`
\(< =>\left[{}\begin{matrix}x=0\\x+3=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)
b)
`x-2x^2 =0`
`<=>x(1-2x)=0`
\(< =>\left[{}\begin{matrix}x=0\\1-2x=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\end{matrix}\right.\)
c)
`(x-7)(2x+3)=x(x-7)`
`<=>(x-7)(2x+3)-x(x-7)=0`
`<=>(x-7)(2x+3-x)=0`
`<=>(x-7)(x+3)=0`
\(< =>\left[{}\begin{matrix}x-7=0\\x+3=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=7\\x=-3\end{matrix}\right.\)
d)
`(x-2)(x+3)=(x-2)(3x-1)`
`<=>(x-2)(x+3)-(x-2)(3x-1)=0`
`<=>(x-2)(x+3-3x+1)=0`
`<=>(x-2)(-2x+4)=0`
\(< =>\left[{}\begin{matrix}x-2=0\\-2x+4=0\end{matrix}\right.\\ < =>x=2\)
2
11 tháng 1 2023
Bài `1:`
`h)(3/4x-1)(5/3x+2)=0`
`=>[(3/4x-1=0),(5/3x+2=0):}=>[(x=4/3),(x=-6/5):}`
______________
Bài `2:`
`b)3x-15=2x(x-5)`
`<=>3(x-5)-2x(x-5)=0`
`<=>(x-5)(3-2x)=0<=>[(x=5),(x=3/2):}`
`d)x(x+6)-7x-42=0`
`<=>x(x+6)-7(x+6)=0`
`<=>(x+6)(x-7)=0<=>[(x=-6),(x=7):}`
`f)x^3-2x^2-(x-2)=0`
`<=>x^2(x-2)-(x-2)=0`
`<=>(x-2)(x^2-1)=0<=>[(x=2),(x^2=1<=>x=+-2):}`
`h)(3x-1)(6x+1)=(x+7)(3x-1)`
`<=>18x^2+3x-6x-1=3x^2-x+21x-7`
`<=>15x^2-23x+6=0<=>15x^2-5x-18x+6=0`
`<=>(3x-1)(5x-1)=0<=>[(x=1/3),(x=1/5):}`
`j)(2x-5)^2-(x+2)^2=0`
`<=>(2x-5-x-2)(2x-5+x+2)=0`
`<=>(x-7)(3x-3)=0<=>[(x=7),(x=1):}`
`w)x^2-x-12=0`
`<=>x^2-4x+3x-12=0`
`<=>(x-4)(x+3)=0<=>[(x=4),(x=-3):}`
2
11 tháng 1 2023
`m)(1-x)(5x+3)=(3x-7)(x-1)`
`<=>(1-x)(5x+3)+(1-x)(3x-7)=0`
`<=>(1-x)(5x+3+3x-7)=0`
`<=>(1-x)(8x-4)=0<=>[(x=1),(x=1/2):}`
`p)(2x-1)^2-4=0`
`<=>(2x-1-2)(2x-1+2)=0`
`<=>(2x-3)(2x+1)=0<=>[(x=3/2),(x=-1/2):}`
`r)(2x-1)^2=49`
`<=>(2x-1-7)(2x-1+7)=0`
`<=>(2x-8)(2x+6)=0<=>[(x=4),(x=-3):}`
`t)(5x-3)^2-(4x-7)^2=0`
`<=>(5x-3-4x+7)(5x-3+4x-7)=0`
`<=>(x+4)(9x-10)=0<=>[(x=-4),(x=10/9):}`
`u)x^2-10x+16=0`
`<=>x^2-8x-2x+16=0`
`<=>(x-2)(x-8)=0<=>[(x=2),(x=8):}`
Cái j đấy ! xin cậu sau viết đề có tâm nhé
Sửa đề :\(3x+1-3=x\)
\(3x-2=x\Leftrightarrow2x-2=0\Leftrightarrow2x=2\Leftrightarrow x=1\)