\(\left(x-5\right)^6=\left(x-5\right)^8\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^8=0\)
\(\Rightarrow\left(x-5\right)^6\left[1-\left(x-5\right)^2\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-5\right)^6=0\\1-\left(x-5\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=5\\\left(x-5\right)^2=\left(\pm1\right)^2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=5\\x-5=1\\x-5=-1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=5\\x=6\\x=4\end{cases}}\)
P/s: 2 dòng cuối bạn thay \(\hept{\begin{cases}\\\\\end{cases}}\)thành \(\orbr{\begin{cases}\\\end{cases}}\)nhé
b, Gọi ƯCLN\((a,a\cdot b+4)\)là d. Ta có :
\(a⋮d\Rightarrow a\cdot b⋮d\)
\(a\cdot b+4⋮d\)
\(\Rightarrow a\cdot b+4-a\cdot b⋮d\)
\(\Rightarrow4⋮d\)
\(\Rightarrow d\inƯ(4)\)
Mà a là số lẻ
\(\Rightarrow d\ne\pm2;\pm4\)
\(\Rightarrow d\in\left\{1;-1\right\}\)
\(\Rightarrow d=1\)
\(\RightarrowƯCLN(a,a\cdot b+4)=1\)
Vậy : ....
