Question

Tìm x nguyên biết (x-1)^5=(x-1)^3

Answer 1

\(\left(x-1\right)^5=\left(x-1\right)^3\\ \Rightarrow\left(x-1\right)^5-\left(x-1\right)^3=0\\ \Rightarrow\left(x-1\right)^3\left[\left(x-1\right)^2-1\right]=0\\ \Rightarrow\left(x-1\right)^3\left(x-1-1\right)\left(x-1+1\right)=0\\ \Rightarrow\left(x-1\right)^3\left(x-2\right).x=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)