Question

1, Tìm x \(\in Z\): /3x-1/ \(\leq \) 27

2, Có bao nhiêu cặp số nguyên (x;y) biết : / x / + 2/ y / = 2017

Answer 1

Ta có:\(\left|3x-1\right|\le27\)

\(\Rightarrow\left[{}\begin{matrix}3x-1\le27\\1-3x\le27\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}3x\le28\\-3x\le26\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x\le\dfrac{28}{3}\\x\le\dfrac{26}{-3}\end{matrix}\right.\)

Mà \(x \in Z\) \(\Rightarrow x\in\left[{}\begin{matrix}\left\{9;8;7;6;5;4;3;2;1\right\}\\\left\{-8;-7;-6;-3;-2;-1\right\}\end{matrix}\right.\)