Question

1. Tìm các số nguyên x và y biết:

\(|x-2|\)+ \(|x.y-6|\)= 0

Answer 1

Vì: \(\left\{{}\begin{matrix}\left|x-2\right|\ge0\\\left|xy-6\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x-2\right|+\left|xy-6\right|\ge0\)

mà theo đề thì: \(\left|x-2\right|+\left|xy-6\right|=0\)

=> \(\left\{{}\begin{matrix}\left|x-2\right|=0\\\left|xy-6\right|=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=2\\xy=6\Leftrightarrow2y=6\Leftrightarrow y=3\end{matrix}\right.\)

Vậy x= 2 và y = 3

Answer 2

\(\left|x-2\right|+\left|x.y-6\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\x.y-6=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\2.y-6=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)

Vậy \(x=2;y=3\)