Đặt \(t=2x^2+3x-1\) thì pt trở thành :
\(t\left(t-5\right)=-4\) \(\Leftrightarrow t^2-5t+4=0\)
\(\Leftrightarrow t^2-t-4t+4=0\)
\(\Leftrightarrow\left(t-1\right)\left(t-4\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}t=1\\t=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x^2+3x-1=1\\2x^2+3x-1=4\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}2x^2+3x-2=0\\2x^2+3x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)\left(x+2\right)=0\\\left(2x+5\right)\left(x-1\right)=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=-2\\x=-\frac{5}{2}\\x=1\end{matrix}\right.\) ( TM )
\(\Leftrightarrow\left(2x^2+3x-1\right)^2-5\left(2x^2+3x-1\right)+4=0\)
\(\Leftrightarrow\left(2x^2+3x-1-1\right)\left(2x^2+3x-1-4\right)=0\)
\(\Leftrightarrow\left(2x^2+3x-2\right)\left(2x^2+3x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x^2+3x-2=0\\2x^2+3x-5=0\end{matrix}\right.\)
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