\(\left(2x^2+3x-1\right)^2-5\left(2x^2+3x+3\right)+24=0\)(1)
Đặt \(2x^2+3x+1=a\)
Thay vào (1) ta được \(\left(a-2\right)^2-5\left(a+2\right)+24=0\)
\(\Leftrightarrow a^2-4a+4-5a-10+24=0\)
\(\Leftrightarrow a^2-9a+18=0\)
\(\Leftrightarrow a^2-3a-6a+18=0\)
\(\Leftrightarrow\left(a-3\right)\left(a-6\right)=0\Leftrightarrow\left[{}\begin{matrix}a=3\\a=6\end{matrix}\right.\)
Suy ra \(\left[{}\begin{matrix}2x^2+3x+1=3\\2x^2+3x+1=6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x^2+3x-2=0\\2x^2+3x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0,5\\x=-2\end{matrix}\right.\\\left[{}\begin{matrix}x=1\\x=-2,5\end{matrix}\right.\end{matrix}\right.\)
Vậy \(x\in\left\{0,5;-2,5;1;-2\right\}\)
Phân tích đến đây r nha: \(\left(4x^3+16x^2+11x-10\right)\left(x-1\right)=0\)