Question

giải bất phương trình x⁴ - 5x² + 2x+3 < 0

Answer 1

\(\Leftrightarrow\left(x^4+x^3-3x^2\right)-\left(x^3+x^2-3x\right)-\left(x^2+x-3\right)< 0\)

\(\Leftrightarrow x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-1\left(x^2+x-3\right)< 0\)

\(\Leftrightarrow\left(x^2-x-1\right)\left(x^2+x-3\right)< 0\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{-1-\sqrt{13}}{2}< x< \dfrac{1-\sqrt{5}}{2}\\\dfrac{-1+\sqrt{13}}{2}< x< \dfrac{1+\sqrt{5}}{2}\end{matrix}\right.\)