Vì: \(\begin{cases}\left|x+3y-1\right|\ge0\\\left|2y-\frac{1}{2}\right|^{200}\ge0\end{cases}\)\(\Rightarrow\left|x+3y-1\right|+\left|2y-\frac{1}{2}\right|^{200}\ge0\)
Nên: \(\left|x+3y-1\right|+\left|2y-\frac{1}{2}\right|^{200}=0\)
\(\Leftrightarrow\begin{cases}x+3y-1=0\\2y-\frac{1}{2}=0\end{cases}\)
\(\Leftrightarrow\begin{cases}x=1-3y=1-3\cdot\frac{1}{4}=\frac{1}{4}\\y=\frac{1}{4}\end{cases}\)
\(\Leftrightarrow x=y=\frac{1}{4}\)
\(\left|x+3y-1\right|+\left|2y-\frac{1}{2}\right|^{200}=0\)
\(\Rightarrow\left|x+3y-1\right|=0\) và \(\left|2y-\frac{1}{2}\right|^{200}=0\)
+) \(\left|2y-\frac{1}{2}\right|^{200}=0\)
\(\Rightarrow2y-\frac{1}{2}=0\)
\(\Rightarrow2y=\frac{1}{2}\)
\(\Rightarrow y=\frac{1}{4}\)
+) \(\left|x+3y-1\right|=0\)
\(\Rightarrow x+3y-1=0\)
\(\Rightarrow x+3.\frac{1}{4}=1\)
\(\Rightarrow x+\frac{3}{4}=1\)
\(\Rightarrow x=\frac{1}{4}\)
Vậy \(x=\frac{1}{4},y=\frac{1}{4}\)
