Question

Giải pt :

\(\left(x^2+5x\right)^2-2\left(x^2+5x\right)=24\)

Answer 1

Đặt \(x^2+5x=t\), ta được :

\(t^2-2t-24=0\)

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}t=6\\t=-4\end{matrix}\right..\)

Khi \(t=6,\) ta được :

\(x^2+5x-6=0\)

\(\Leftrightarrow x^2-x+6x-6=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-6\end{matrix}\right.\)

Khi \(t=-4\) ta được :

\(x^2+5x+4=0\)

\(\Leftrightarrow x^2+x+4x+4=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4\end{matrix}\right.\)

Vậy .....