Question

tìm x biết: (x-1) mũ x+2=(x-1|) mũ x+6

Answer 1

ta có: \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\Leftrightarrow\left(x-1\right)^{x+6}-\left(x-1\right)^{x+2}=0\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^{x+4}-1\right]=0\)

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

Vậy x = 1 hoặc x = 0

Học tốt nhé ^3^

Answer 2

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

[(x-1)^x].(x-1)^2=[(x-1)^x].(x-1)^6

     (x-1)^2=(x-1)^6

      (X-1)^2=(x-1)^2.(x-1)^4

              1=(x-1)^4

             1=x-1

             1+1=x

               2=x

 Nhớ k cho mình nha

Answer 3

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

\(\Rightarrow\)( x - 1 )^{x + 2} - ( x - 1 )^{x + 6} = 0

\(\Rightarrow\)( x - 1 )^x . ( x - 1 )² - ( x - 1 )^x . ( x - 1 )⁶ = 0

\(\Rightarrow\)( x - 1 )^x . [ ( x - 1 )² - ( x - 1 )⁶ ] = 0

\(\Rightarrow\)( x - 1 )^x = 0 hoặc ( x - 1 )² - ( x - 1 )⁶ = 0

\(\Rightarrow\)x - 1 = 0 hoặc ( x - 1 )² - ( x - 1 )⁶ = 0

\(\Rightarrow\)x = 1 hoặc x = 0

Vậy : x = 1 hoặc x = 0