Question

Tìm số x thuộc Z, biết :

( x - 2 )^{2010 =} ( x - 2 )²⁰¹²

Answer 1

\(\left(x-2\right)^{2010}=\left(x-2\right)^{2012}\)

\(\Rightarrow\left(x-2\right)^{2010}-\left(x-2\right)^{2012}=0\)

\(\Rightarrow\left(x-2\right)^{2010}\left[1-\left(x-2\right)^2\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^{2010}=0\\1-\left(x-2\right)^2=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^2=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x-2=\pm1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)