Tìm x biết :
\(|3x-1|=|x+3|\)
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LN
1
SS
25 tháng 6 2019
\(\left(x-2\right)^3+\left(3\text{x}-1\right)\left(3\text{x}+1\right)=\left(x+1\right)^3\)
\(\Leftrightarrow\left(x-2\right)^3+\left(3\text{x}-1\right)\left(3\text{x}+1\right)-\left(x+1\right)^3=0\)
\(\Leftrightarrow\left(x^3-6\text{x}^2+12\text{x}-8\right)+\left(9\text{x}^2-1\right)-\left(x^3+3\text{x}^2+3\text{x}+1\right)=0\)
\(\Leftrightarrow x^3-6\text{x}^2+12\text{x}-8+9\text{x}^2-1-x^3-3\text{x}^2-3\text{x}-1=0\)
\(\Leftrightarrow\left(x^3-x^3\right)+\left(-6\text{x}^2+9\text{x}^2-3\text{x}^2\right)+\left(12\text{x}-3\text{x}\right)+\left(-8-1-1\right)=0\)
\(\Leftrightarrow9\text{x}-10=0\)
\(\Leftrightarrow9\text{x}=10\Leftrightarrow x=\frac{10}{9}\)
Vậy x = \(\frac{10}{9}\)
HP
0
KH
2
10 tháng 8 2021
x2( x + 1 ) + 2x( x + 1 ) = 0 <=> x( x + 1 )( x + 2 ) = 0 <=> x = 0 hoặc x = -1 hoặc x = -2
x( 3x - 1 ) - 5( 1 - 3x ) = 0 <=> x( 3x - 1 ) + 5( 3x - 1 ) = 0 <=> ( 3x - 1 )( x + 5 ) = 0 <=> x = 1/3 hoặc x = -5
QA
10 tháng 8 2021
Trả lời:
1, \(x^2\left(x+1\right)+2x\left(x+1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x+2\right)=0\)
\(\Leftrightarrow x=0;x=-1;x=-2\)
Vậy x = 0; x = - 1; x = - 2 là nghiệm của pt.
2, \(x\left(3x-1\right)-5\left(1-3x\right)=0\)
\(\Leftrightarrow x\left(3x-1\right)+5\left(3x-1\right)=0\)
\(\Leftrightarrow\left(3x-1\right)\left(x+5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}3x-1=0\\x+5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=-5\end{cases}}}\)
Vậy x = 1/3; x = - 5 là nghiệm của pt.
29 tháng 10 2021
1.
a) \(=x^2-6x+9+3x^2-15x=4x^2-21x+9\)
b) \(=9x^2+12x+4-x^2+9=8x^2+12x+13\)
2.
a) \(\Leftrightarrow x^2+8x+16-x^2+4-5=0\\ \Leftrightarrow8x=-15\\ \Leftrightarrow x=-\dfrac{15}{8}\)
b) \(\Leftrightarrow9x^2-6x+1-8x^2+12x-2x+3-5-x^2=0\\ \Leftrightarrow4x=1\\ \Leftrightarrow x=\dfrac{1}{4}\)
20 tháng 9 2021
\(1,\\ \left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\\ \Leftrightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=8\end{matrix}\right.\)
\(2,\\ a,\left|2x-3\right|>5\Leftrightarrow\left[{}\begin{matrix}2x-3< -5\\2x-3>5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x< -1\\x>4\end{matrix}\right.\\ b,\left|3x-1\right|\le7\Leftrightarrow\left[{}\begin{matrix}3x-1\le7\\1-3x\le7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\le\dfrac{8}{3}\\x\ge-2\end{matrix}\right.\\ c,\cdot x< -\dfrac{3}{2}\\ \Leftrightarrow5-3x+\left(-2x-3\right)=7\Leftrightarrow2-5x=7\Leftrightarrow x=-1\left(ktm\right)\\ \cdot-\dfrac{3}{2}\le x\le\dfrac{5}{3}\\ \Leftrightarrow\left(5-3x\right)+\left(2x+3\right)=7\Leftrightarrow8-x=7\Leftrightarrow x=1\left(tm\right)\\ \cdot x>\dfrac{5}{3}\\ \Leftrightarrow\left(3x-5\right)+\left(2x+3\right)=7\Leftrightarrow5x-2=7\Leftrightarrow x=\dfrac{9}{5}\left(tm\right)\\ \Leftrightarrow S=\left\{1;\dfrac{9}{5}\right\}\)
H
12 tháng 12 2021
a) 2x(3x+1) – (2x+3)(3x-2) = 12
\(\Leftrightarrow6x^2+2x-\left(6x^2-4x+9x-6\right)=12\)
\(\Leftrightarrow6x^2+2x-6x^2+4x-9x+6=12\)
\(\Leftrightarrow-3x+6=12\)
\(\Leftrightarrow-3x=6\)
\(\Leftrightarrow x=-2\)
vậy x = -2
b) (x+2)2 – (x-3)(x+3) = 5
\(\Leftrightarrow\left(x+2\right)^2-\left(x^2-9\right)=5\)
\(\Leftrightarrow x^2+4x+4-x^2+9-5=0\)
\(\Leftrightarrow4x+8=0\)
\(\Leftrightarrow4x=-8\)
\(\Leftrightarrow x=-2\)
Vậy x = -2
Ta có: |3x - 1| = |x + 3|
=> \(\orbr{\begin{cases}3x-1=x+3\\1-3x=x+3\end{cases}}\)
=> \(\orbr{\begin{cases}2x=4\\4x=-2\end{cases}}\)
=> \(\orbr{\begin{cases}x=2\\x=-\frac{1}{2}\end{cases}}\)
\(\left|3x-1\right|=\left|x+3\right|\)
=> \(\orbr{\begin{cases}3x-1=x+3\\3x-1=-x-3\end{cases}}\)
=>\(\orbr{\begin{cases}2x=4\\4x=-2\end{cases}}\)=> \(\orbr{\begin{cases}x=2\\x=-\frac{1}{2}\end{cases}}\)