* \(x^2-8x+12=0\Leftrightarrow x^2-2x-6x+12=0\)
\(\Leftrightarrow x\left(x-2\right)-6\left(x-2\right)=0\Leftrightarrow\left(x-2\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-6=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=6\end{matrix}\right.\) vậy \(x=2;x=6\)
* \(x^2+5x-14=0\Leftrightarrow x^2-2x+7x-14=0\)
\(\Leftrightarrow x\left(x-2\right)+7\left(x-2\right)=0\Leftrightarrow\left(x+7\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+7=0\\x-2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=2\end{matrix}\right.\) vậy \(x=-7;x=2\)
* \(16x^2-81=0\Leftrightarrow16\left(x^2-\dfrac{81}{16}\right)=0\Leftrightarrow x^2-\dfrac{81}{16}=0\)
\(\Leftrightarrow x^2=\dfrac{81}{16}\) \(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{81}{16}}\\x=-\sqrt{\dfrac{81}{16}}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=\dfrac{-9}{4}\end{matrix}\right.\) vậy \(x=\dfrac{9}{4};x=\dfrac{-9}{4}\)
+ \(x^2-8x+12=0\)
\(\Rightarrow\left(x^2-2.4x+16\right)-4=0\)
\(\Rightarrow\left(x-4\right)^2-4=0\)
\(\Rightarrow\left(x-4\right)^2=4\)
\(\Rightarrow\left[{}\begin{matrix}x-4=2\\x-4=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=6\\x=2\end{matrix}\right.\)
+ \(16x^2-81=0\)
\(\Rightarrow16x^2-9^2=0\)
\(\Rightarrow16x^2=9^2\)
\(\Rightarrow x^2=\dfrac{81}{16}\)
\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{81}{16}}\\x=-\sqrt{\dfrac{81}{16}}\end{matrix}\right.\)
