Giải:
a) \(3x\left(x-1\right)+1-x=0\)
\(\Leftrightarrow3x\left(x-1\right)+\left(1-x\right)=0\)
\(\Leftrightarrow3x\left(x-1\right)-\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy ...
b) \(25-x^2+2x-1=0\)
\(\Leftrightarrow25-\left(x^2-2x+1\right)=0\)
\(\Leftrightarrow5^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(5-x+1\right)\left(5+x-1\right)=0\)
\(\Leftrightarrow\left(6-x\right)\left(4+x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}6-x=0\\4+x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)
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c) \(\left(x-3\right)^2-\left(x+3\right)\left(x-1\right)=7\)
\(\Leftrightarrow x^2-6x+9-\left(x^2+2x-3\right)=7\)
\(\Leftrightarrow x^2-6x+9-x^2-2x+3=7\)
\(\Leftrightarrow12-8x=7\)
\(\Leftrightarrow8x=12-7\)
\(\Leftrightarrow8x=5\)
\(\Leftrightarrow x=\dfrac{5}{8}\)
Vậy ...