a) \(\left(x-\dfrac{2}{3}\right)\left(x\cdot7+\dfrac{1}{4}\right)=0\)
\(\Rightarrow\left(x-\dfrac{2}{3}\right)\left(7x+\dfrac{1}{4}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{2}{3}=0\\7x+\dfrac{1}{4}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{1}{28}\end{matrix}\right.\)
Vậy \(x_1=-\dfrac{1}{28};x_2=\dfrac{2}{3}\)
b) \(\left(x+1\right)\left(x-2\right)< 0\)
\(\left\{{}\begin{matrix}x+1< 0\\x-2>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x< -1\\x>2\end{matrix}\right.\) \(\Rightarrow x\in\varnothing\)
\(\left\{{}\begin{matrix}x+1< 0\\x-2< 0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x>-1\\x< 2\end{matrix}\right.\) \(\Rightarrow x\in\left\{0;1\right\}\)
Vậy \(x\in\left\{0;1\right\}\)
c) \(\left(x-2\right)\cdot x+\dfrac{2}{3}>0\)
\(\Rightarrow x^2-2x+\dfrac{2}{3}>0\)
\(\Leftrightarrow3x^2-6x+2>0\)
\(\Leftrightarrow3x^2-6x+2=0\)
... giải tiếp
