a, \(x^3-x^2=4x^2-8x+4\)
\(\Rightarrow x^3-x^2-4x^2+8x-4=0\)
\(\Rightarrow x^2\left(x-1\right)-4x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^2-2x-2x+4\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x-2\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
b, \(\left(x-1\right)\left(x^2+x+1\right)=7\)
\(\Rightarrow x^3-1=7\Rightarrow x^3=2^3\Rightarrow x=2\)
c, \(2\left(x+5\right)-x^2-5x=0\)
\(\Rightarrow2\left(x+5\right)-x\left(x+5\right)=0\)
\(\Rightarrow\left(x+5\right)\left(2-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+5=0\\2-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
d, \(x^2-3x=-2\)
\(\Rightarrow x^2-x-2x+2=0\)
\(\Rightarrow x\left(x-1\right)-2\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
Chúc bạn học tốt!!!
