a.
\(3x^2-2x+\dfrac{1}{3}=0\)
\(\Leftrightarrow9x^2-6x+1=0\)
\(\Leftrightarrow\left(3x-1\right)^2=0\)
\(\Leftrightarrow3x-1=0\)
\(\Leftrightarrow x=\dfrac{1}{3}\)
b.
\(\left(2x-1\right)^2-\left(x+2\right)^2=0\)
\(\Leftrightarrow\left(2x-1+x+2\right)\left(2x-1-x-2\right)=0\)
\(\Leftrightarrow\left(3x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+1=0\\x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=3\end{matrix}\right.\)
a, \(3x^2-2x+\dfrac{1}{3}=0\)
\(\Leftrightarrow x^2-\dfrac{2}{3}x+\dfrac{1}{9}=0\)
\(\Leftrightarrow x^2-2.x.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{3}\right)^2=0\)
\(\Leftrightarrow x=\dfrac{1}{3}\)
b, \(\left(2x-1\right)^2-\left(x+2\right)^2=0\)
\(\Leftrightarrow\left(2x-1-x-2\right)\left(2x-1+x+2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\3x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{3}\end{matrix}\right.\)
