a: =>(2x-1)(2x-1+x-3)=0
=>(2x-1)(3x-4)=0
=>x=1/2 hoặc x=4/3
d: =>(x-2)(x-3)=0
=>x=2 hoặc x=3
b: =>2x-2x2+1-x+3x=2
=>-2x2+4x-3=0
=>2x2-4x+3=0
\(\text{Δ}=\left(-4\right)^2-4\cdot2\cdot3=16-24=-8< 0\)
Do đó: Phương trình vô nghiệm
\(a,\left(2x-1\right)^2+\left(x-3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(2x-1-x-3\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-1=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\x=4\end{matrix}\right.\)
Câu còn lại làm tương tự
d, \(\Leftrightarrow x^2-2x-3x+6=0\)
\(\Leftrightarrow x\left(x-2\right)-3\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
a) \(PT\Leftrightarrow\left(2x-1\right)\left(2x-1+x-3\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\3x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{4}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{1}{2};\dfrac{4}{3}\right\}\)
b) \(PT\Leftrightarrow2x-2x^2+1-x+3x=2\)
\(\Leftrightarrow2x^2-4x+1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1-\dfrac{1}{\sqrt{2}}\\x=1+\dfrac{1}{\sqrt{2}}\end{matrix}\right.\)
Vậy: \(S=\left\{1-\dfrac{1}{\sqrt{2}};1+\dfrac{1}{\sqrt{2}}\right\}\)
c) Chắc đề bài là \(2\left(x-5\right)\left(x+2\right)=x^2-5x\)
\(\Leftrightarrow2x^2+4x-10x-20=x^2-5x\)
\(\Leftrightarrow x^2-x-20=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
Vậy: \(S=\left\{5;-4\right\}\)
d) \(PT\Leftrightarrow\left(x-3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=2\end{matrix}\right.\)
Vậy: \(S=\left\{3;2\right\}\)
a, \(\Leftrightarrow\left(2x-1\right)\left(2x-1+x-3\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-1=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\x=4\end{matrix}\right.\)
