\(\left(x-1\right)\left(x-4\right)\left(x-5\right)\left(x-8\right)+36=0\)
\(\left[\left(x-1\right)\left(x-8\right)\right]\left[\left(x-4\right)\left(x-5\right)\right]+36=0\)
\(\left(x^2-9x+8\right)\left(x^2-9x+20\right)+36=0\)
Đặt \(a=x^2-9x+14\)ta có :
\(\left(a-6\right)\left(a+6\right)+36=0\)
\(a^2-6^2+36=0\)
\(a^2=0\)
Thay \(a=x^2-9x+14\)ta có :
\(\left(x^2-9x+14\right)^2=0\)
\(\Leftrightarrow x^2-9x+14=0\)
\(\Leftrightarrow x^2-2x-7x+14=0\)
\(\Leftrightarrow x\left(x-2\right)-7\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-7\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-2=0\\x-7=0\end{cases}\Rightarrow\orbr{\begin{cases}x=2\\x=7\end{cases}}}\)
Vậy,...........
\(\left(x-1\right)\left(x-4\right)\left(x-5\right)\left(x-8\right)+36=0\)
\(\left(x-1\right)\left(x-8\right)\left(x-4\right)\left(x-5\right)+36=0\)
\(\left(x^2-9x+8\right)\left(x^2-9x+20\right)+36=0\)
Đặt \(x^2-9x+14=t\)
\(\left(t-6\right)\left(t+6\right)+36=0\)
\(t^2-36+36=0\)
\(\Rightarrow t^2=0\)
\(\Rightarrow x^2-9x+16=0\)
\(\Rightarrow x^2-2.\frac{9}{2}x+\frac{81}{4}=\frac{17}{4}\)
\(\Rightarrow\left(x-\frac{9}{2}\right)^2=\frac{17}{4}\)
\(\Rightarrow x=\hept{\begin{cases}\sqrt{\frac{17}{4}}+\frac{9}{2}\\-\sqrt{\frac{17}{4}}+\frac{9}{2}\end{cases}}\)
