a ) \(x^2-11x-26=0\)
\(\Leftrightarrow x^2-13x+2x-26=0\)
\(\Leftrightarrow x\left(x-13\right)+2\left(x-13\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-13\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-13=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=13\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-2\\x=13\end{matrix}\right.\)
b ) \(2x^2+7x-4=0\)
\(\Leftrightarrow2\left(x^2+\dfrac{7}{2}x-2\right)=0\)
\(\Leftrightarrow x^2+\dfrac{7}{2}x-2=0\)
\(\Leftrightarrow x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{81}{16}=0\)
\(\Leftrightarrow\left(x+\dfrac{7}{4}\right)^2=\dfrac{81}{16}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{7}{4}=\dfrac{9}{4}\\x+\dfrac{7}{4}=-\dfrac{9}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-4\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-4\end{matrix}\right.\)
c ) \(\left(x-2\right)\left(x-3\right)+\left(x-2\right)-1=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)+x-3=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-2+1\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
