Question

Tìm x biết 

(x-7)^x+1 - (x-7)^x+11  = 0

Answer 1

\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

\(\Leftrightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-7=0\\\left(x-7\right)^{10}-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=7\\\left(x-7\right)=1;x-7=-1\end{cases}}\)

Vậy x = 7; x = 8; x = 6

Answer 2

x =7 hoặc 8 hoặc 6