Question

tim x biet:(x-1)^x+2 =(x-1)^x+6 ?

Answer 1

\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\)

\(\Rightarrow\left(x-1\right)^{x+2}.\left[1-\left(x-1\right)^4\right]=0\)

\(\Rightarrow\left[\begin{array}{nghiempt}\left(x-1\right)^{x+2}=0\\1-\left(x-1\right)^4=0\end{array}\right.\)

\(+\)

Nếu \(\left(x-1\right)^{x+2}=0\Rightarrow x-1=0\Rightarrow x=1\)

\(+\)

Nếu \(1-\left(x-1\right)^4=0\Rightarrow\left(x-1\right)^4=1=\left(\pm1\right)^4\)

\(\Rightarrow\left[\begin{array}{nghiempt}x-1=1\\x-1=-1\end{array}\right.\)

\(\Rightarrow\left[\begin{array}{nghiempt}x=2\\x=0\end{array}\right.\)

Vậy \(x\in\left\{0;1;2\right\}\)