Question

giai phuong trinh sau

/x-7/^15+/x-8/^16=1

Answer 1

\(\left|x-7\right|^{15}+\left|x-8\right|^{16}=1\)

Ta có: \(\hept{\begin{cases}\left|x-7\right|^{15}\ge0\\\left|x-8\right|^{16}\ge0\end{cases}}\)mà \(\left|x-7\right|^{15}+\left|x-8\right|^{16}=1\)

\(\Rightarrow\orbr{\begin{cases}\left|x-7\right|^{15}=1;\left|x-8\right|^{16}=0\\\left|x-7\right|^{15}=0;\left|x-8\right|^{16}=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=8\\x=0\end{cases}}\)