Question

Giải PT : \(x^4+4x^3-10x^2-28x-15=0\)

Answer 1

\(x^4+4x^3+4x^2-14x^2-28x-15=0\)

\(\Leftrightarrow\left(x^2+2x\right)^2-14\left(x^2+2x\right)-15=0\)

Đặt \(x^2+2x=a\Rightarrow a^2-14a-15=0\Rightarrow\left[{}\begin{matrix}a=-1\\a=15\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x^2+2x=-1\\x^2+2x=15\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2+2x+1=0\\x^2+2x-15=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-1\\x=-5\\x=3\end{matrix}\right.\)