Question

Giải phương trình:

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

Answer 1

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

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

Đặt \(x^2+x=t\)

=> ta có phương trình:

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

\(\Leftrightarrow t^2-2t+1-25=0\)

\(\Leftrightarrow\left(t-1\right)^2-5^2=0\)

\(\Leftrightarrow\left(t-1-5\right)\left(t-1+5\right)=0\)

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

\(\Leftrightarrow\)\(\left[{}\begin{matrix}t-6=0\\t+4=0\end{matrix}\right.\)\(\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}x^2+x-6=0\\x^2+x+4=0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}\left(x-2\right)\left(x+3\right)=0\\\left(x+\frac{1}{2}\right)^2+\frac{15}{16}=0\end{matrix}\right.\)

Tự làm nốt