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\(3\left(x-2\right)+4=5x-2\left(x-1\right)\\ \Leftrightarrow3x-6+4=5x-2x+2\\ \Leftrightarrow0x=4\left(vôlý\right)\)
Vậy pt vô nghiệm
\(2\left(x-2\right)-3\left(1-2x\right)=5\\ \Leftrightarrow2x-4-3+6x=5\\ \Leftrightarrow8x=12\\ \Leftrightarrow x=\dfrac{3}{2}\)
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- Ta có: \(\left(x^2-1\right).\left(x+2\right).\left(x-3\right)=\left(x-1\right).\left(x^2-4\right).\left(x+5\right)\)
\(\Leftrightarrow\left(x-1\right).\left(x+1\right).\left(x+2\right).\left(x-3\right)=\left(x-1\right).\left(x-2\right).\left(x+2\right).\left(x+5\right)\)
\(\Leftrightarrow\left(x-1\right).\left(x+1\right).\left(x+2\right).\left(x-3\right)-\left(x-1\right).\left(x-2\right).\left(x+2\right).\left(x+5\right)=0\)
\(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left[\left(x+1\right).\left(x-3\right)-\left(x-2\right).\left(x+5\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left[\left(x^2-2x-3\right)-\left(x^2+3x-10\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left(x^2-2x-3-x^2-3x+10\right)=0\)
\(\Leftrightarrow\left(x-1\right).\left(x+2\right).\left(-5x+7\right)=0\)
+ \(x-1=0\)\(\Leftrightarrow\)\(x=1\left(TM\right)\)
+ \(x+2=0\)\(\Leftrightarrow\)\(x=-2\left(TM\right)\)
+ \(-5x+7=0\)\(\Leftrightarrow\)\(-5x=-7\)\(\Leftrightarrow\)\(x=\frac{7}{5}\left(TM\right)\)
Vậy \(S=\left\{-2,1,\frac{7}{5}\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)(3x-1)(4x-8)=0
⇔3x-1=0 hoặc 4x-8=0
1.3x-1=0⇔3x=1⇔x=1/3
2.4x-8=0⇔4x=8⇔x=2
phương trình có 2 nghiệm:x=1/3 và x=2
b)(x-2)(1-3x)=0
⇔x-2=0 hoặc 1-3x=0
1.x-2=0⇔x=2
2.1-3x=0⇔-3x=1⇔x=-1/3
phương trình có 2 nghiệm:x=2 và x=-1/3
c)(x-3)(x+4)-(x-3)(2x-1)=0
⇔(x+4)(2x-1)=0
⇔x+4=0 hoặc 2x-1=0
1.x+4=0⇔x=-4
2.2x-1=0⇔2x=1⇔x=1/2
phương trình có hai nghiệm:x=-4 và x=1/2
d)(x+1)(x+2)=2x(x+2)
⇔(x+1)(x+2)-2x(x+2)=0
⇔2x(x+1)=0
⇔2x=0 hoặc x+1=0
1.2x=0⇔x=0
2.x+1=0⇔x=-1
phương trình có 2 nghiệm:x=0 và x=-1
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\(\left(x-1\right)^2-1+x^2=\left(1-x\right).\left(x+3\right)\)
\(x^2-2x+1-1+x^2=x-x^2+3-3x\)
\(2x^2-2x=-2x-x^2+3\)
\(2x^2+x^2-2x+2x=3\)
\(3x^2=3\)
\(\Rightarrow x^2=1\Rightarrow x=\left\{1;-1\right\}\)
(x-1)^2 - 1 + x^2= (1-x)(x+3)
\(\Leftrightarrow\)x^2-2x+1-1+x^2=x+3-x^2+3x
\(\Leftrightarrow\)2x^2-2x=4x-x^2+3
\(\Leftrightarrow\)3x^2-6x=3
\(\Leftrightarrow\)3x(x-2)=3
\(\orbr{\begin{cases}3x=3\\x-2=3\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x=5\end{cases}}\)
Vậy pt có 2 nghiệm x=1 và x=5