\(\left(x-6\right)^6=\left(x-6\right)^8\)
\(\Leftrightarrow\left(x-6\right)^6.\left(x-5\right).\left(x-7\right)\)
\(\Leftrightarrow\hept{\begin{cases}x-6=0\\x-5=0\\x-7=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=6\\x=5\\x=7\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=6\\x=5\\x=7\end{cases}}\)
\(\left(x-6\right)^6=\left(x-6\right)^8\)
\(\Leftrightarrow\left(x-6\right)^6=\left(x-6\right)^{6+2}\)
\(\Leftrightarrow\left(x-6\right)^6=\left(x-6\right)^6\times\left(x-6\right)^2\)
\(\Leftrightarrow\left(x-6\right)^2=1\)
\(\Leftrightarrow\left(x-6\right)^2=1^2\)
\(\Leftrightarrow x-6=1\)
\(\Leftrightarrow x=1+6\)
\(\Leftrightarrow x=7\)
\(\left(x-6\right)^6=\left(x-6\right)^8\)
\(\Rightarrow\left(x-6\right)^6-\left(x-6\right)^8=0\)
\(\Rightarrow\left(x-6\right)^6\left[1-\left(x-6\right)^2\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-6\right)^6=0\\1-\left(x-6\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-6=0\\\left(x-6\right)^2=1\end{cases}}\)
<=> x-6 =0 hoặc x-6 =1 hoặc x-6 =-1
<=> x=6 hoặc x=7 hoặc x=5
