Question

Tìm số nguyên x, y biết :

a) -1/3 < x/36 < y/18 < -1/8

b) 9/36 < x/8 < y/7 < 13/28

Answer 1

a)

\(-\dfrac{1}{3}< \dfrac{x}{36}\Rightarrow-36< 3x\Rightarrow x>-12\)

\(\dfrac{y}{18}< \dfrac{-1}{8}\Rightarrow8y< -18\Rightarrow y< -\dfrac{18}{8}< -2\) (do y là số nguyên )

\(\Rightarrow2y< -4\)

\(\dfrac{x}{36}< \dfrac{y}{18}\Rightarrow18x< 36y\Rightarrow x< 2y\)

\(\Rightarrow-12< x< -4\)

\(\Rightarrow x\in\left\{-11;-10;....;-3;-4\right\}\)

\(\Rightarrow y\in\left\{-11;-10;...;-3;-4\right\}\)