Question

(x-1)^x+2=(x-1)^x+6,tìm x.help me.huhu

 

Answer 1

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

=>(x-1)(x-2)x=0

hay \(x\in\left\{0;1;2\right\}\)

Answer 2

`(x-1)^(x+2)=(x-1)^(x+6)`

`<=>(x-1)^(x+2) - (x-1)^(x+6) =0`

`<=> (x-1)^(x+2) - (x-1)^(x+2) * (x-1)^4 =0`

`<=>  (x-1)^(x+2) * ( 1 - (x-1)^4) =0`

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

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^4=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0+1\\\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=1\\\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\end{matrix}\right.\)

Answer 3

thank you