Question

a, ( x - 2 )( x + \(\dfrac{4}{11}\) ) > 0

b, x² - x < 0

Answer 1

\(\left(x-2\right)\left(x+\dfrac{4}{11}\right)>0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2>0\Rightarrow x>2\\x+\dfrac{4}{11}>0\Rightarrow x>-\dfrac{4}{11}\end{matrix}\right.\\\left\{{}\begin{matrix}x-2< 0\Rightarrow x< 2\\x+\dfrac{4}{11}< 0\Rightarrow x< -\dfrac{4}{11}\end{matrix}\right.\end{matrix}\right.\)

Vậy \(x< 2\) hoặc \(x>-\dfrac{4}{11}\)

\(x^2-x< 0\)

\(\Rightarrow x\left(x-1\right)< 0\)

Với mọi giá trị \(x\in R\) thì \(x-1< x\)

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

Vậy \(x>0\) hoặc \(x< -1\)

Answer 2

Lập đàn cầu thánh nhân :^)