Question

(x-1)⁵= (x-1)⁷

Answer 1

\(\Leftrightarrow\left(x-1\right)^5\cdot\left[\left(x-1\right)^2-1\right]=0\)

\(\Leftrightarrow\left(x-1\right)^5\cdot\left(x-2\right)\left(x-1+1\right)=0\)

hay \(x\in\left\{0;1;2\right\}\)

Answer 2

\(\left(x-1\right)^5=\left(x-1\right)^7\)

\(\left(x-1\right)^7-\left(x-1\right)^5=0\)

\(\left(x-1\right)^5\left[\left(x-1\right)^2-1\right]=0\)

\(\left(x-1\right)^5=0\) hoặc \(\left(x-1\right)^2-1=0\)

*) \(\left(x-1\right)^5=0\)

\(x-1=0\)

\(x=0+1\)

\(x=1\)

*) \(\left(x-1\right)^2-1=0\)

\(\left(x-1\right)^2=0+1\)

\(\left(x-1\right)^2=1\)

\(\left(x-1\right)^2=1^2\) hoặc \(\left(x-1\right)^2=\left(-1\right)^2\)

\(x-1=1\) hoặc \(x-1=-1\)

+) \(x-1=1\)

\(x=1+1\)

\(x=2\)

+) \(x-1=-1\)

\(x=-1+1\)

\(x=0\)

Vậy \(x=0;x=1;x=2\)