Ta có: \(3x-\left(x-2\right)\left(x+2\right)< 3x^2+x\)
\(\Leftrightarrow3x-x^2+4-3x^2-x< 0\)
\(\Leftrightarrow-4x^2+2x+4< 0\)
\(\Leftrightarrow4x^2-2x-4< 0\)
\(\Leftrightarrow\left(2x\right)^2-2\cdot2x\cdot\dfrac{1}{2}+\dfrac{1}{4}< \dfrac{17}{4}\)
\(\Leftrightarrow\left(2x-\dfrac{1}{2}\right)^2< \dfrac{17}{4}\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-\dfrac{1}{2}< \dfrac{\sqrt{17}}{2}\\2x-\dfrac{1}{2}>\dfrac{-\sqrt{17}}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x< \dfrac{\sqrt{17}+1}{2}\\2x>\dfrac{-\sqrt{17}+1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< \dfrac{\sqrt{17}+1}{4}\\x>\dfrac{-\sqrt{17}+1}{4}\end{matrix}\right.\Leftrightarrow\dfrac{-\sqrt{17}+1}{4}< x< \dfrac{\sqrt{17}+1}{4}\)
Bạn học cái "trong trái ngoài cùng" chưa bạn nhỉ?
