Đáp án:
$a)\left[\begin{array}{l} x=0\\x=1\end{array} \right.\\ b) \left[\begin{array}{l} x=0\\x=1\\x=-1\end{array} \right.\\ c) \left[\begin{array}{l} x=-1\\x=2\end{array} \right.\\ d)\left[\begin{array}{l} x=\dfrac{1}{5}\\x=3\end{array} \right.\\ e) x=0.$
Giải thích các bước giải:
$a)3x^2-x=0\\ \Leftrightarrow 3x(x-1)=0\\ \Leftrightarrow \left[\begin{array}{l} 3x=0\\x-1=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=0\\x=1\end{array} \right.\\ b)x-x^3=0\\ \Leftrightarrow x(1-x^2)=0\\ \Leftrightarrow x(1-x)(1+x)=0\\ \Leftrightarrow \left[\begin{array}{l} x=0\\1-x=0\\1+x=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=0\\x=1\\x=-1\end{array} \right.\\ c)x(x-2)+x-2=0\\ \Leftrightarrow x(x-2)+(x-2)=0\\ \Leftrightarrow (x+1)(x-2)=0\\ \Leftrightarrow \left[\begin{array}{l} x+1=0\\x-2=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=-1\\x=2\end{array} \right.\\ d)5x(x-3)-x+3=0\\ \Leftrightarrow 5x(x-3)-(x-3)=0\\ \Leftrightarrow (5x-1)(x-3)=0\\ \Leftrightarrow \left[\begin{array}{l} 5x-1=0\\x-3=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=\dfrac{1}{5}\\x=3\end{array} \right.\\ e)x^3+x=0\\ \Leftrightarrow x(x^2+1)=0\\ \Leftrightarrow \left[\begin{array}{l} x=0\\x^2+1(\text{Vô nghiệm})\end{array} \right.\\ \Leftrightarrow x=0.$
