Nhân 4 lên rồi đặt 2x=y
\(8x^3+9.4x^2+7.4x-24=0\)
\(\Leftrightarrow y^3+9y^2+14y-24=0\) cho gọn hệ số dẽ ghép
\(y^2\left(y-1\right)+10y\left(y-1\right)+24y-24=\left(y-1\right)\left(y^2+10y+24\right)\)
\(\Leftrightarrow\left[\begin{matrix}y-1=0\Rightarrow y=1\Rightarrow x=\frac{1}{2}\\y^2+10y+24=0\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow y^2+2.5y+25=\left(y+5\right)^2=1\Rightarrow\left[\begin{matrix}y=-6\\y=-4\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=-3\\x=-2\end{matrix}\right.\)
Kết luận: \(\left[\begin{matrix}x=\frac{1}{2}\\x=-2\\x=-3\end{matrix}\right.\)
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