Question

|x-y|+|y+9/25|=0

Answer 1

Ta có :

\(\left|x-y\right|\ge0\forall x;y\\ \left|y+\dfrac{9}{25}\right|\ge0\forall y\\ \Rightarrow\left|x-y\right|+\left|y+\dfrac{9}{25}\right|\ge0\forall x;y\\ \Rightarrow\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\\ \Rightarrow\left\{{}\begin{matrix}\left|x-y\right|=0\\\left|y+\dfrac{9}{25}\right|=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x-y=0\\y+\dfrac{9}{25}=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=y\\y=-\dfrac{9}{25}\end{matrix}\right.\\ Vậyx=y=-\dfrac{9}{25}\)