Question

Tìm x,y biết:|x-2018y|+(y-1)²⁰¹⁸=0

Answer 1

\(\text{Vì}\hept{\begin{cases}\left|x-2018y\right|\ge0\\\left(y-1\right)^{2018}\ge0\end{cases}\Rightarrow\left|x-2018y\right|+\left(y-1\right)^{2018}\ge0}\)

Mà theo đề VT = 0

Nên dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x-2018y=0\\y-1=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=2018\\y=1\end{cases}}\)

Vậy x = 20 8 ; y = 1

Answer 2

\(\left|x-2018\right|+\left(y-1\right)^{2018}=0.\)

\(Nx:\)\(\left|x-2018\right|\ge0;\left(y-1\right)^{2018}\ge0\)

\(\Rightarrow VT=0\Leftrightarrow\left|x-2018\right|=0;\left(y-1\right)^{2018}=0\)

\(\left|x-2018\right|=0\Leftrightarrow x-2018=0\Leftrightarrow x=2018\)

\(\left(y-1\right)^{2018}=0\Leftrightarrow y-1=0\Leftrightarrow y=1\)