`a)`
\(\left(x-3\right)^{23}=\left(x-3\right)^7\\ \rightarrow\left(x-3\right)^{23}-\left(x-3\right)^7=0\\ \rightarrow\left(x-3\right)^7\cdot\left(x-3\right)^{16}-\left(x-3\right)^7\cdot1=0\\ \rightarrow\left(x-3\right)^7\cdot\left[\left(x-3\right)^{16}-1\right]=0\\ \rightarrow\left[{}\begin{matrix}\left(x-3\right)^7=0\\\left(x-3\right)^{16}-1=0\end{matrix}\right.\\ \rightarrow\left[{}\begin{matrix}x-3=0\\x-3=1\end{matrix}\right.\\ \rightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
các câu sau làm tương tự nhé!
`a) (x-3)^23 = (x-3)^7`
`=> `\(\dfrac{\left(x-3\right)^{23}}{\left(x-3\right)^7}=1\)
`<=>(x-3)^16 =1`
`<=>`\(\left[{}\begin{matrix}x-3=1\\x-3=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1+3=4\\x=-1+3=2\end{matrix}\right.\)
`b)(x-2)^11 = (x-2)^3`
`=>`\(\dfrac{\left(x-2\right)^{11}}{\left(x-2\right)^3}=1\)
`=> (x-2)^8 =1`
`=> `\(\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1+2=3\\x=-1+2=1\end{matrix}\right.\)
`c)(x-4)^21 =(x-4)^7`
`<=>`\(\dfrac{\left(x-4\right)^{21}}{\left(x-4\right)^7}=1\)
`<=> (x-4)^14 =1`
`<=>`\(\left[{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)
`d)(x-2)^9 = (x-2)^4`
`<=>`\(\dfrac{\left(x-2\right)^9}{\left(x-2\right)^4}=1\)
`=> (x-2)^5 =1`
`=> x-2=1`
`=> x=1+2=3`
