\(x^4-10x^3+25x^2=36\)
➜\(x^4-10x^3=25x^2-36=0\)
➜\(x^3\left(x-3\right)-7x^2\left(x-3\right)+4x\left(x-3\right)+12\left(x-3\right)=0\)
➜\(\left(x-3\right)\left(x^3-7x^2+x+12\right)=0\)
➜\(\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(x-6\right)=0\)
➜\(\left[{}\begin{matrix}x-3=0\\x-2=0\\x+1=0\\x-6=0\end{matrix}\right.\text{➜}\left[{}\begin{matrix}x=3\\x=2\\x=-1\\x=6\end{matrix}\right.\)
Vậy..................................................
Ta có: \(x^4-10x^3+25x^2=36\Leftrightarrow x^4-10x^3+25x^2-36=0\Leftrightarrow x^4+x^3-11x^3-11x^2+36x^2-36=0\)
\(\Leftrightarrow x^3\left(x+1\right)-11x^2\left(x+1\right)+36\left(x+1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^3-11x^2+36x-36\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\\x=3\\x=6\end{matrix}\right.\)
\(x^4-10x^3+25x^2=36\\ \Leftrightarrow x^4-10x^3+25x^3-36=0\\ \Leftrightarrow x^3\cdot\left(x-3\right)-7x^2\cdot\left(x-3\right)+4x\cdot\left(x-3\right)+12\cdot\left(x-3\right)=0\\ \Leftrightarrow\left(x-3\right)\cdot\left(x^3-7x^2+4x+12\right)=0\\ \Leftrightarrow\left(x-3\right)\cdot\left[x^2\cdot\left(x-2\right)-5x\cdot\left(x-2\right)-6\cdot\left(x-2\right)\right]=0\\ \Leftrightarrow\left(x-3\right)\cdot\left[\left(x-2\right)\cdot\left(x^2-5x-6\right)\right]=0\\ \Leftrightarrow\left(x-3\right)\cdot\left(x-2\right)\cdot\left(x+1\right)\cdot\left(x-6\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\\x+1=0\\x-6=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=3\\x=2\\x=-1\\x=6\end{matrix}\right.\)
