Question

tìm x,y biết

 \(\left|x+y-\frac{1}{100}\right|=\left|-x\right|-\left|y\right|-\left|\frac{1}{100}\right|\)
 

Answer 1

\(VT=\left|x-\left(-y+\frac{1}{100}\right)\right|\ge\left|x\right|-\left|-y+\frac{1}{100}\right|\)

\(\ge\left|x\right|-\left(\left|-y\right|+\left|\frac{1}{100}\right|\right)=\left|-x\right|-\left|y\right|-\left|\frac{1}{100}\right|=VP\)

Dấu "=" xảy ra khi \(\hept{\begin{cases}\left|x\right|\ge\left|-y+\frac{1}{100}\right|\\x\left(-y+\frac{1}{100}\right)\ge0\\-y.\frac{1}{100}\ge0\end{cases}}\Leftrightarrow\hept{\begin{cases}x+y\ge\frac{1}{100}\\x\ge\frac{1}{100}\\y\le0\end{cases}}\)

Vậy pt có nghiệm \(x\ge\frac{1}{100};y\le0\) thoả mãn \(x+y\ge\frac{1}{100}\)