Question

tìm x   |x-199|^200 + |x-200|^201 = 1

Answer 1

\(\left|x-199\right|^{200}+\left|x-200\right|^{201}=1\left(1\right)\)

Vì \(\left\{{}\begin{matrix}\left|x-199\right|^{200}\ge0\\\left|x-200\right|^{201}\ge0\end{matrix}\right.\) nên ta có :

\(TH1:\left\{{}\begin{matrix}\left|x-199\right|^{200}=1\\\left|x-200\right|^{201}=0\end{matrix}\right.\Rightarrow x-200=0\Rightarrow x=200\) thỏa \(\left(1\right)\)

\(TH2:\left\{{}\begin{matrix}\left|x-199\right|^{200}=0\\\left|x-200\right|^{201}=1\end{matrix}\right.\Rightarrow x-199=0\Rightarrow x=199\) thỏa \(\left(1\right)\)

Vậy \(x\in\left\{199;200\right\}\)