Tìm y biết 2y(y-1/7)=0

a, \(x.\left(x-\dfrac{4}{7}\right)>0\)

\(\Rightarrow\left\{{}\begin{matrix}x>0\\x-\dfrac{4}{7}>0\end{matrix}\right.\) hay \(\left\{{}\begin{matrix}x< 0\\x-\dfrac{4}{7}< 0\end{matrix}\right.\)

+, Xét \(\left\{{}\begin{matrix}x>0\\x-\dfrac{4}{7}>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>0\\x>\dfrac{4}{7}\end{matrix}\right.\Rightarrow x>\dfrac{4}{7}\)(1)

+, Xét \(\left\{{}\begin{matrix}x< 0\\x-\dfrac{4}{7}< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 0\\x< \dfrac{4}{7}\end{matrix}\right.\Rightarrow x< 0\)(2)

Vậy \(x>\dfrac{4}{7}\) và \(x< 0\)

b, \(\left(x-\dfrac{2}{5}x^2\right)< 0\)

\(\Rightarrow x.\left(1-\dfrac{2}{5}x\right)< 0\)

\(\Rightarrow\left\{{}\begin{matrix}x>0\\1-\dfrac{2}{5}x< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>0\\\dfrac{2}{5}x>1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>0\\x>2,5\end{matrix}\right.\)

\(\Rightarrow x>2,5\)

Vậy \(x>2,5\)

c, \(\left(x-\dfrac{2}{5}\right).\left(x+\dfrac{3}{7}\right)>0\)

\(\Rightarrow\left\{{}\begin{matrix}x-\dfrac{2}{5}>0\\x+\dfrac{3}{7}>0\end{matrix}\right.\) hay \(\left\{{}\begin{matrix}x-\dfrac{2}{5}< 0\\x+\dfrac{3}{7}< 0\end{matrix}\right.\)

+, Xét \(\left\{{}\begin{matrix}x-\dfrac{2}{5}>0\\x+\dfrac{3}{7}>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>\dfrac{2}{5}\\x>\dfrac{-3}{7}\end{matrix}\right.\) \(\Rightarrow x>\dfrac{2}{5}\)

+, Xét \(\left\{{}\begin{matrix}x-\dfrac{2}{5}< 0\\x+\dfrac{3}{7}< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< \dfrac{2}{5}\\x< \dfrac{-3}{7}\end{matrix}\right.\) \(\Rightarrow x< \dfrac{-3}{7}\)

Vậy \(x>\dfrac{2}{5};x< \dfrac{-3}{7}\)

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