Question

cho hso \(y=\dfrac{x}{x^2-x+1}\). Tìm tập nghiệm bpt 2x.y'-3y\(^2\)\(\ge\) 0

Answer 1

\(y'=\dfrac{2x^2-x-x^2+x-1}{\left(x^2-x+1\right)^2}=\dfrac{x^2-1}{\left(x^2-x+1\right)^2}\)

\(\dfrac{2x^3-2x}{\left(x^2-x+1\right)^2}-3.\dfrac{x^2}{\left(x^2-x+1\right)^2}\ge0\)

\(\Leftrightarrow2x^3-2x-3x^2\ge0\Leftrightarrow x^2+2x\le0\Leftrightarrow x\left(x+2\right)\le0\)

\(\Leftrightarrow-2\le x\le0\)