tìm x biết :
x : 0,2 + x :0 , 25 = 4 , 05
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5: =>4x^2-1/9=0
=>(2x-1/3)(2x+1/3)=0
=>x=1/6 hoặc x=-1/6
6: =>x-1=2
=>x=3
7:=>(2x-1)^3=-27
=>2x-1=-3
=>2x=-2
=>x=-1
8: =>1/8(x-1)^3=-125
=>(x-1)^3=-1000
=>x-1=-10
=>x=-9
3: =>(5x-5)^2-4=0
=>(5x-7)(5x-3)=0
=>x=3/5 hoặc x=7/5
4: =>(5x-1)^2=0
=>5x-1=0
=>x=1/5
1: =>(3x-1)(2x-1)=0
=>x=1/3 hoặc x=1/2
2: =>x^2(2x-3)-4(2x-3)=0
=>(2x-3)(x^2-4)=0
=>(2x-3)(x-2)(x+2)=0
=>x=3/2;x=2;x=-2
`@` `\text {Answer}`
`\downarrow`
`1,`
\(2x\left(3x-1\right)+1-3x=0\)
`<=> 2x(3x - 1) - 3x + 1 = 0`
`<=> 2x(3x - 1) - (3x - 1) = 0`
`<=> (2x - 1)(3x-1) = 0`
`<=>`\(\left[{}\begin{matrix}2x-1=0\\3x-1=0\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}2x=1\\3x=1\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy, `S = {1/2; 1/3}`
`2,`
\(x^2\left(2x-3\right)+12-8x=0\)
`<=> x^2(2x - 3) - 8x + 12 =0`
`<=> x^2(2x - 3) - (8x - 12) = 0`
`<=> x^2(2x - 3) - 4(2x - 3) = 0`
`<=> (x^2 - 4)(2x - 3) = 0`
`<=>`\(\left[{}\begin{matrix}x^2-4=0\\2x-3=0\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x^2=4\\2x=3\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x^2=\left(\pm2\right)^2\\x=\dfrac{3}{2}\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=\pm2\\x=\dfrac{3}{2}\end{matrix}\right.\)
Vậy, `S = {+-2; 3/2}`
`3,`
\(25\left(x-1\right)^2-4=0\)
`<=> 25(x-1)(x-1) - 4 = 0`
`<=> 25(x^2 - 2x + 1) - 4 = 0`
`<=> 25x^2 - 50x + 25 - 4 = 0`
`<=> 25x^2 - 15x - 35x + 21 = 0`
`<=> (25x^2 - 15x) - (35x - 21) = 0`
`<=> 5x(5x - 3) - 7(5x - 3) = 0`
`<=> (5x - 7)(5x - 3) = 0`
`<=>`\(\left[{}\begin{matrix}5x-7=0\\5x-3=0\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}5x=7\\5x=3\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=\dfrac{7}{5}\\x=\dfrac{3}{5}\end{matrix}\right.\)
Vậy, `S = {7/5; 3/5}`
`4,`
\(25x^2-10x+1=0\)
`<=> 25x^2 - 5x - 5x + 1 = 0`
`<=> (25x^2 - 5x) - (5x - 1) = 0`
`<=> 5x(5x - 1) - (5x - 1) = 0`
`<=> (5x - 1)(5x-1)=0`
`<=> (5x-1)^2 = 0`
`<=> 5x - 1 = 0`
`<=> 5x = 1`
`<=> x = 1/5`
Vậy,` S = {1/5}.`
|0,2 . x - 3,1| + |0,2 . x + 3,1| = 0
Ta có: \(\hept{\begin{cases}\left|0,2.x-3,1\right|\ge0\\\left|0,2.x+3,1\right|\ge0\end{cases}}\)
Mà theo đề bài: |0,2 . x - 3,1| + |0,2 . x + 3,1| = 0
\(\Rightarrow\hept{\begin{cases}0,2.x-3,1=0\\0,2.x+3,1=0\end{cases}}\Rightarrow\hept{\begin{cases}0,2.x=3,1\\0,2.x=-3,1\end{cases}}\Rightarrow\hept{\begin{cases}x=15,5\\x=-15,5\end{cases}}\)
Vay x = 15,5 ; -15,5
\(\frac{x}{0,5}+\frac{x}{0,25}+\frac{x}{0,2}=5,5\)
\(\Rightarrow x\cdot2+x\cdot4+x\cdot5=5,5\)
\(\Rightarrow x\cdot(2+4+5)=5,5\)
\(\Rightarrow x\cdot11=5,5\)
\(\Rightarrow x=5,5\div11=0,5\)
\(20\%x+0,4x=12\)
\(\Rightarrow0,2x+0,4x=12\)
\(\Rightarrow(0,2+0,4)x=12\)
\(\Rightarrow0,6x=12\)
\(\Rightarrow x=20\)
`1,(4x^3+3x^3):x^3+(15x^2+6x):(-3x)=0`
`<=> 4 + 3 + (-5x) + (-2)=0`
`<=> -5x+5=0`
`<=>-5x=-5`
`<=>x=1`
`2,(25x^2-10x):5x +3(x-2)=4`
`<=> 5x - 2 + 3x-6=4`
`<=> 8x -8=4`
`<=> 8x=12`
`<=>x=12/8`
`<=>x=3/2`
`3,(3x+1)^2-(2x+1/2)^2=0`
`<=> [(3x+1)-(2x+1/2)][(3x+1)+(2x+1/2)]=0`
`<=>( 3x+1-2x-1/2)(3x+1+2x+1/2)=0`
`<=>( x+1/2) (5x+3/2)=0`
`@ TH1`
`x+1/2=0`
`<=>x=0-1/2`
`<=>x=-1/2`
` @TH2`
`5x+3/2=0`
`<=> 5x=-3/2`
`<=>x=-3/2 : 5`
`<=>x=-15/2`
`4, x^2+8x+16=0`
`<=>(x+4)^2=0`
`<=>x+4=0`
`<=>x=-4`
`5, 25-10x+x^2=0`
`<=> (5-x)^2=0`
`<=>5-x=0`
`<=>x=5`
a) |0,2x - 3,1| = 6,3
\(0,2x-3,1=\pm6,3\)
Th1:
0,2x - 3,1 = 6,3
0,2x = 6,3 + 3,1
0,2x = 9,4
x = 9,4 : 0,2
x = 47
Th2:
0,2x - 3,1 = - 6,3
0,2x = - 6,3 + 3,1
0,2x = - 3,2
x = - 3,2 : 0,2
x = - 16
Vậy x = 47 hoặc x = - 16
b) |12,1x + 12,1 . 0,1| = 12,1
|12,1(x + 0,1)| = 12,1
\(12,1\left(x+0,1\right)=\pm12,1\)
Th1:
12,1(x + 0,1) = 12,1
x + 0,1 = 1
x = 1 - 0,1
x = 0,9
Th2:
12,1(x + 0,1) = - 12,1
x + 0,1 = - 1
x = - 1 - 0,1
x = - 1,1
Vậy x = 0,9 hoặc x = - 1,1
c) |0,2x - 3,1| + |0,2.x + 3,1| = 0
|0,2x - 3,1| + |0,2x + 3,1| \(\ge\) |0,2x - 3,1 + 0,2x + 3,1| = 0,4x
mà |0,2x - 3,1| + |0,2.x + 3,1| = 0
=> x = 0
x:(0,2+0,25)=4,05
X:0,45=4,05
x=4,05:0,45=9
\(\Leftrightarrow x:\left(0,2+0,25\right)=4,05\)
\(\Leftrightarrow x:0,45=4,05\)
\(\Leftrightarrow x=4,05\div0,45\)
\(\Rightarrow x=9\)