\(\left(x^2-4x+3\right)\left(x^2-6x+8\right)=8\)
\(\left(x^2-3x-x+3\right)\left(x^2-4x-2x+8\right)=8\)
\(\left[x\left(x-3\right)-1\left(x-3\right)\right]\left[x\left(x-4\right)-2\left(x-4\right)\right]=8\)
\(\left(x-1\right)\left(x-3\right)\left(x-2\right)\left(x-4\right)=8\)
\(\left(x-1\right)\left(x-4\right)\left(x-2\right)\left(x-3\right)=8\)
\(\left(x^2-5x+4\right)\left(x^2-5x+6\right)-8=0\)
Đặt \(t=x^2-5x+4\)
\(t\left(t+2\right)-8=0\)
\(t^2+2t-8=0\)
\(t^2+4t-2t-8=0\)
\(t\left(t+4\right)-2\left(t+4\right)=0\)
\(\left(t+4\right)\left(t-2\right)=0\)
\(\orbr{\begin{cases}t+4=0\\t-2=0\end{cases}}\)
\(\orbr{\begin{cases}t=-4\\t=2\end{cases}}\)
\(\orbr{\begin{cases}x^2-5x+4=-4\\x^2-5x+4=2\end{cases}}\)
\(\orbr{\begin{cases}x^2-5x+8=0\left(ptvn\right)\\x^2-5x+2=0\end{cases}}\)
\(x^2-5x+2=0\)
\(\orbr{\begin{cases}x=\frac{5+\sqrt{17}}{2}\\x=\frac{5-\sqrt{17}}{2}\end{cases}}\)
