(X+1/2)*(2/3-2X)=0
Tìm X
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\(a,\Leftrightarrow\left(x+2\right)\left(x+2-x+3\right)=0\\ \Leftrightarrow5\left(x+2\right)=0\Leftrightarrow x=-2\\ b,\Leftrightarrow2x\left(x-1\right)^2=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\\ c,\Leftrightarrow\left(x-1-2x-1\right)\left(x-1+2x+1\right)=0\\ \Leftrightarrow3x\left(-x-2\right)=0\Leftrightarrow-3x\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
a: Ta có: \(\left(x-\dfrac{2}{5}\right)\left(x+\dfrac{2}{7}\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{2}{5}\\x< -\dfrac{2}{7}\end{matrix}\right.\)
\(\Leftrightarrow2x^2-11x+5-2x^2+10x=25\Leftrightarrow-x=20\Leftrightarrow x=-20\)
\(\Leftrightarrow\left(x-2021\right)\left(x-5\right)-\left(x-2021\right)=0\\ \Leftrightarrow\left(x-2021\right)\left(x-6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2021\\x=6\end{matrix}\right.\)
\(\left(2x+m\right)\left(x-1\right)-2x^2+mx+m-2=0\)
\(\Leftrightarrow2x^2-2x+mx-m-2x^2+mx+m-2=0\)
\(\Leftrightarrow\left(2m-2\right)x-2=0\)
\(\Leftrightarrow\left(2m-2\right)x=2\)
\(\Leftrightarrow x=\dfrac{2}{2m-2}\)
Để phương trình đã cho có nghiệm âm thì:
\(\dfrac{2}{2m-2}< 0\)
\(\Leftrightarrow2m-2< 0\)
\(\Leftrightarrow2m< 2\)
\(\Leftrightarrow m< 1\)
Vậy \(m< 1\) thì phương trình đã cho có nghiệm âm.
\(\left(2x+m\right)\left(x-1\right)-2x^2+mx+m-2=0\)
\(\Leftrightarrow2x^2+mx-2x-m-2x^2+mx+m-2=0\)
\(\Leftrightarrow\left(2m-2\right)x-2=0\left(1\right)\)
+) Nếu \(m=1\)\(\rightarrow\left(1\right)\Leftrightarrow0x-2=0\left(V_{n_o}\right)\)
+) Nếu \(m\ne1\rightarrow x=\dfrac{2}{2m-2}\)
Để \(x< 0\Leftrightarrow\dfrac{2}{2m-2}< 0\) mà \(2>0\Leftrightarrow2m-2< 0\Leftrightarrow m< 1\)
\(\dfrac{1}{3}x+\dfrac{2}{3}\left(x-1\right)=0\\ \dfrac{1}{3}x+\dfrac{2}{3}x-\dfrac{2}{3}=0\\ x=\dfrac{2}{3}\)
Ta có: \(\left(x-2\right)^3-x\left(x-1\right)\left(x+1\right)+x\left(7x-6\right)=0\)
\(\Leftrightarrow x^3-6x^2+12x-8-x^3+x+7x^2-6x=0\)
\(\Leftrightarrow x^2+7x-8=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-8\\x=1\end{matrix}\right.\)
\(\left(\frac{x+1}{2}\right)\cdot\left(\frac{2}{3-2X}\right)=0\)
=> \(\orbr{\begin{cases}\frac{x+1}{2}=0\\\frac{2}{3-2x}=0\end{cases}}\)
(=)\(\orbr{\begin{cases}x+1=0\\3-2x=0\end{cases}}\)
(=)\(\orbr{\begin{cases}x=-1\\x=\frac{3}{2}\end{cases}}\)
Vậy x= - 1 hoặc x=\(\frac{3}{2}\)