\(\left(x-1\right)\left(x-3\right)\left(x+5\right)\left(x+7\right)=297\)
\(\Rightarrow\left[\left(x-1\right)\left(x+5\right)\right]\left[\left(x-3\right)\left(x+7\right)\right]=297\)
\(\Rightarrow\left[x^2+4x-5\right]\left[x^2+4x-5-16\right]=297\)
Đặt \(x^2+4x-5=t\)
\(\Rightarrow t\left(t-16\right)=297\)
\(\Rightarrow t^2-16t+64=297+64\)
\(\Rightarrow\left(t+8\right)^2=361\)
\(\Rightarrow\left[{}\begin{matrix}t+8=19\\t+8=-19\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}t=11\\t=-27\end{matrix}\right.\)
Ta có : \(\left(x-1\right)\left(x-3\right)\left(x+5\right)\left(x+7\right)=297\)
\(\Leftrightarrow\left[\left(x-1\right)\left(x+5\right)\right]\left[\left(x-3\right)\left(x+7\right)\right]=297\)
\(\Leftrightarrow\left(x^2-x+5x-5\right)\left(x^2-3x+7x-21\right)=297\)
\(\Leftrightarrow\left(x^2+4x-5\right)\left(x^2+4x-21\right)=297\)
\(\Leftrightarrow\left(x^2+4x-13+8\right)\left(x^2+4x-13-8\right)=297\)
\(\Leftrightarrow\left(x^2+4x-13\right)^2-64=297\)
\(\Leftrightarrow\left(x^2+4x-13\right)^2=361\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+4x-13=19\\x^2+4x-13=-19\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+4x+4-17=19\\x^2+4x+4-17=-19\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x+2\right)^2-17=19\\\left(x+2\right)^2-17=-19\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x+2\right)^2=36\\\left(x+2\right)^2=-2\left(VL\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=6\\x+2=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)
