tim cap so nguyen x,y biet `3|x-2017|+1 = 2/(|y-2018|+1)`

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1. Đáp án: $(x,y)\in\{(2017, 2019), (2017, 2017)\}$

   Giải thích các bước giải:

   Ta có:

   $|y-2018|+1\ge 0+1=1$

   $\to \dfrac{2}{|y-2018|+1}\le\dfrac21=2$

   $\to 3|x-2017|+1\le 2$

   Mà $x\in Z\to 3|x-2017|+1\in Z$

   Lại có $3|x-2017|+1\ge 3\cdot 0+1=1$

   $\to 1\le 3|x-2017|+1\le 2$

   Vì $3|x-2017|+1$ chia $3$ dư $1$

   $\to 3|x-2017|+1=1$

   $\to 3|x-2017|=0$

   $\to |x-2017|=0$

   $\to x-2017=0$

   $\to x=2017$

   $\to \dfrac{2}{|y-2018|+1}=3\cdot 0+1=1$

   $\to |y-2018|+1=2$

   $\to |y-2018|=1$

   $\to y-2018=1\to y=2019$

   Hoặc $y-2018=-1\to y=2017$

   Trả lời