a) \(2x^2=x\Rightarrow2x^2-x=0\Rightarrow x\left(2x-1\right)\Rightarrow\left[{}\begin{matrix}x=0\\2x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\frac{1}{2}\end{matrix}\right.\)
b) \(x^2-\frac{1}{36}=0\Rightarrow\left(x+\frac{1}{6}\right)\left(x-\frac{1}{6}\right)=0\Rightarrow\left[{}\begin{matrix}x+\frac{1}{6}=0\\x-\frac{1}{6}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\frac{1}{6}\\x=\frac{1}{6}\end{matrix}\right.\)
c) \(x^2-14x+49=0\Rightarrow\left(x-7\right)^2=0\Rightarrow x-7=0\Rightarrow x=7\)
d) \(x^3-3x^2+3x-1=0\Rightarrow\left(x^3-1\right)-\left(3x^2-3x\right)=0\Rightarrow\left(x-1\right)\left(x^2+x+1\right)-3x\left(x-1\right)=0\Rightarrow\left(x-1\right)\left(x^2+x+1-3x\right)=0\Rightarrow x-1=0\Rightarrow x=-1\)
e) \(x\left(x-2\right)-5x+10=0\Rightarrow x\left(x-2\right)-5\left(x-2\right)=0\Rightarrow\left(x-2\right)\left(x-5\right)=0\Rightarrow\left[{}\begin{matrix}x-2=0\\x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)
a) \(2x^2=x\)
\(\Leftrightarrow2x^2-x=0\)
\(\Leftrightarrow2x\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
b)\(x^2-\frac{1}{36}=0\)
\(\Leftrightarrow x^2-\left(\frac{1}{6}\right)^2=0\)
\(\Leftrightarrow\left(x-\frac{1}{6}\right)\left(x+\frac{1}{6}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{6}=0\\x+\frac{1}{6}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{6}\\x=-\frac{1}{6}\end{matrix}\right.\)
c)\(\text{ x²-14x+49=0}\)
\(\Leftrightarrow x^2-2.7.x+7^2=0\)
\(\Leftrightarrow\left(x-7\right)^2=0\)
\(\Leftrightarrow x-7=0\)
\(\Leftrightarrow x=7\)
d)\(x^3-3x^2+3x-1=0\)
\(\Leftrightarrow(x-1)^3=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
\(\text{e) x(x-2) -5x+10=0}\)
\(\Leftrightarrow x\left(x-2\right)-5\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)
a)\(2x^2=x\)
\(\Leftrightarrow2x^2-x=0\)
\(\Leftrightarrow x\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{1}{2}\end{matrix}\right.\)
\(2x^2=x\)
