Question

Giải phương trình:

\(x\left(x-1\right)\left(x+1\right)\left(x+2\right)-24=0\)

Answer 1

PT \(\Leftrightarrow\left[x\left(x+1\right)\right].\left[\left(x-1\right)\left(x+2\right)\right]-24=0\)

\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)-24=0\)

Đặt \(x^2+x=t\) ta được:

\(t\left(t-2\right)-24=0\Leftrightarrow t^2-2t-24=0\)

\(\Leftrightarrow t^2-6t+4t-24=0\)\(\Leftrightarrow t\left(t-6\right)+4\left(t-6\right)=0\)

\(\Leftrightarrow\left(t-6\right)\left(t+4\right)=0\Leftrightarrow\orbr{\begin{cases}t=6\\t=-4\end{cases}}\)

Suy ra \(\orbr{\begin{cases}x^2+x-6=0\\x^2+x+4=0\end{cases}}\)

Ez rồi.