Question

Tìm x \(\in\)Z sao cho \(\left(x-1\right)^{2016}=\left(1-x\right)^{2018}\)

Answer 1

\(\left(x-1\right)^{2016}=\left(1-x\right)^{2018}\)

\(\Rightarrow\left(x-1\right)^{2016}=-\left(x-1\right)^{2018}\)

\(\Rightarrow\left(x-1\right)^{2016}=\left(x-1\right)^{2018}\)

\(\Rightarrow\left(x-1\right)^{2016}-\left(x-1\right)^{2018}=0\)

\(\Rightarrow\left(x-1\right)^{2016}.\left(1-\left(x-1\right)^2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\left(x-1\right)^{2016}=0\\1-\left(x-1\right)^2=0\end{cases}}\)

nốt nha

Answer 2

\(\left(x-1\right)^{2016}=\left(1-x\right)^{2018}\)

hai vế có mũ là 2016 và 2018 thì đổi ra bằng 0 vì số rất lớn

\(\Rightarrow x\in\left\{1;2\right\}\)