b)\(\left(x-1\right)\left(x+2\right)\left(x+4\right)\left(x+7\right)=16\)
\(\Leftrightarrow\left(x-1\right)\left(x+7\right)\left(x+2\right)\left(x+4\right)=16\)
\(\Leftrightarrow\left(x^2+6x-7\right)\left(x^2+6x+8\right)-16=0\)
Đặt \(x^2+6x+0,5=t\)
\(\Rightarrow\left(t-7,5\right)\left(t+7,5\right)-16=0\)
\(\Rightarrow t^2-56,25-16=0\)
\(\Leftrightarrow t^2-72,25=0\)
\(\Leftrightarrow\left(t-\dfrac{17}{2}\right)\left(t+\dfrac{17}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=\dfrac{17}{2}\\t=-\dfrac{17}{2}\end{matrix}\right.\)
Xét \(t=\dfrac{17}{2}\Rightarrow x^2+6x+0,5=\dfrac{17}{2}\)
\(\Leftrightarrow x^2+6x-8=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3+\sqrt{17}\\x=-3-\sqrt{17}\end{matrix}\right.\)
TT xét \(t=-\dfrac{17}{2}\Rightarrow x=\)-3