\(\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)=18\)
\(\left(x-1\right)\left(x-4\right)\left(x-2\right)\left(x-3\right)=18\)
\(\left(x^2-5x+4\right)\left(x^2-5x+6\right)=18\)
Đặt \(x^2-5x+5=a\)
⇒ \(\left(a-1\right)\left(a+1\right)=18\)
⇒ \(a^2-1=18\)
⇒ \(a=\pm\sqrt{19}\)
...
\(\Leftrightarrow\left(x^2-5x+4\right)\left(x^2-5x+6\right)=18\)
Đặt \(x^2-5x+5=t\)
\(\left(t-1\right)\left(t+1\right)=18\)
\(\Leftrightarrow t^2=19\Leftrightarrow t=\pm\sqrt{19}\)
Với t = căn19 \(\Leftrightarrow x^2-5x+5-\sqrt{19}=0\)
\(\Delta=25-4\left(5-\sqrt{19}\right)=5+4\sqrt{19}\)>0
vậy pt có 2 nghiệm pb
\(x=\dfrac{5\pm\sqrt{5+4\sqrt{19}}}{2}\)
Với t = -căn19 \(\Leftrightarrow x^2-5x+5+\sqrt{19}=0\)
\(\Delta=25-4\left(5+\sqrt{19}\right)=5-4\sqrt{19}\)>0
vậy pt có 2 nghiệm pb
\(x=\dfrac{5\pm\sqrt{5-4\sqrt{19}}}{2}\)
