Question

Tìm các số nguyên dương x biết:

a)\(\dfrac{19}{-23}\)\(< \dfrac{-19}{x}\)\(< \dfrac{19}{-29}\)      b)\(\dfrac{2}{3}\)\(< \dfrac{88}{x}\)\(< \dfrac{11}{16}\)        c)\(\dfrac{4}{x}\)\(< \dfrac{x}{8}\)\(< \dfrac{5}{x}\)

Answer 1

a: =>19/23>19/x>19/29

=>\(x\in\left\{24;25;26;27;28\right\}\)

b: =>88/132<88/x<88/128

=>132>x>128

=>\(x\in\left\{131;130;129\right\}\)

c: =>\(\left\{{}\begin{matrix}\dfrac{4}{x}-\dfrac{x}{8}< 0\\\dfrac{x}{8}-\dfrac{5}{x}< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{32-x^2}{8x}< 0\\\dfrac{x^2-40}{8x}< 0\end{matrix}\right.\)

=>32<x^2<40

=>x=6